Prime Minister David Cameron described the murders of 12 people in Paris as "sickening".
Condemning the attack on the French satirical weekly Charlie Hebdo, he said on Twitter: "We stand with the French people in the fight against terror and defending the freedom of the press."
And he told MPs: "This House and this country stands united with the French people in our opposition to all forms of terrorism and we stand squarely for free speech and democracy.
"These people will never be able to take us off those values."
Deputy Prime Minister Nick Clegg said the killings were a "barbaric attack on freedom of speech".
"My thoughts are with the victims, their families and their colleagues," he said.
Ed Miliband said he felt "horror and outrage" about the attack after Mr Cameron led condemnation in the Commons at prime minister's questions.
"We stand in solidarity with the people of France against this evil terrorist attack by people intent on attacking our democratic way of life and freedom of speech," the Labour leader said.
"We are united in our determination to beat them."
London mayor Boris Johnson said on Twitter: "Shocked and appalled by senseless attack at Charlie Hebdo - London stands with Paris and the people of France against this horrific scourge."
President Barack Obama's spokesman said US officials had been in close contact with the French authorities.
Josh Earnest told CNN the French have been "stalwart allies" in the US fight against Islamic State extremists, adding: "We know they are not going to be cowed by this terrible act."
US ambassador to London, Matthew Barzun said on Twitter: "Terrible news from Charlie Hebdo in Paris. My thoughts and prayers are with the families of the victims."
And Nato general secretary Jens Stoltenberg said: "I strongly condemn the terrorist attack at the office of the Charlie Hebdo magazine in Paris today.
"This was a barbaric act and an outrageous attack on press freedom.
"My thoughts are with the victims and their families.
"We stand in full solidarity with our ally France.
"All Nato allies stand together in the fight against terrorism. Terrorism in all its forms and manifestations can never be tolerated or justified."
Campaigners Index on Censorship condemned the attack.
Index chief executive Jodie Ginsberg said: "The ability to express ourselves freely is fundamental to a free society.
"This includes the freedom to publish, to satirise, to joke, to criticise, even when that might cause offence to others. Those who wish to silence free speech must never be allowed to prevail."
European Commission President Jean-Claude Juncker said he was "profoundly shocked" by the carnage.
In a statement released in French by the European Commission, he said: "I am profoundly shocked by the brutal and inhumane attack on the Charlie Hebdo premises.
"It is an intolerable act, a barbaric act that concerns us all, as humans, and as Europeans.
"My thoughts go out to the victims and their families. I wish to express, both personally and on behalf of the European Commission, our greatest solidarity with France."
Kate Allen, director of Amnesty International UK said: "This is a hideous attack on free speech not just in Paris but everywhere. Journalists are frequently on the frontline and this is another tragic reminder of the deadly risks they so often face."
Baroness Sayeeda Warsi - who was Britain's first female Muslim Cabinet minister - said: "There is no justification for this callous act.
"Thoughts and prayers are with the victims and their families."
Ukip communities spokesman Amjad Bashir said: "This is a horrendous crime which should be condemned unreservedly.
"Those that killed these totally innocent people are disgusting criminals, they are animals.
"These acts of extremism are horrific and totally unjustified, and I condemn them absolutely.
"There are no circumstances and no causes that would make an attack like this justifiable, and, however the attackers try to dress this up, it was an act of pure evil."
In a message on Twitter, the Mayor of Paris, Anne Hidalgo, said: "I have a feeling of absolute horror at the attack which has just been perpetrated against Charlie Hebdo.
"All my compassion to these victims, martyrs of liberty and of the freedom of the press, a pillar of the Republic.
"In the name of Parisians, as well as myself personally, I assure the families and friends of my total solidarity.
"Our country, our city and our democracy are mourning this massacre.
"We must respond to this act by united around the principles of the Republic."
The Union des Organisations Islamiques de France (UOIF), which represents more than 250 Muslim organisations across France, has condemned the killings.
"Charlie Hebdo has just become the target of an appalling attack," the group said in a French-language statement.
"The UOIF condemns, in the strongest possible terms, this criminal attack and these horrible murders.
"The UOIF offers its condolences to the families as well as the employees of Charlie Hebdo."
Professor Bill Durodie, from the University of Bath's department of politics, languages and international studies, an expert in radicalisation, said: "The incident in Paris today is, first and foremost, a tragedy.
"The perpetrators must be apprehended but, more broadly, we must also all reaffirm the importance of absolute freedom of expression in an open society - no matter how offensive this may be to some and, on occasion, how puerile it may become.
"The solution to bad ideas, as the Enlightenment philosopher John Stuart Mill noted, is not censorship but more speech with which to counter them.
"Sadly, the state, in France and here in the UK, as well as the media themselves on occasion, have in recent years been in the vanguard of banning free expression or attempting to regulate ideas they hold to be offensive.
"The French government demonstrated its censorious and anti-Enlightenment outlook in banning Muslim women from wearing the veil in public, while here in the UK various bodies have in recent months banned an art exhibition at the Barbican Centre in London and a public debate at the University of Oxford.
"It is our confusions over such matters that act as a green light to others to take action.
"Over 25 years ago it was only the Ayatollah Khomeini who issued a fatwa against the publication of the Satanic Verses.
"Today, it would seem as though much of Western society has embraced such regulatory impulses through the form of self-censorship. Clarifying these confusions for ourselves will be the first necessary step towards avoiding such incidents again in future."
US President Barack Obama said in a statement: "I strongly condemn the horrific shooting at the offices of Charlie Hebdo magazine that reportedly killed 12 people.
"Our thoughts and prayers are with the victims of this terrorist attack and the people of France at this difficult time.
"France is America's oldest ally, and has stood shoulder to shoulder with the United States in the fight against terrorists who threaten our shared security and the world.
"Time and again, the French people have stood up for the universal values that generations of our people have defended. France, and the great city of Paris where this outrageous attack took place, offer the world a timeless example that will endure well beyond the hateful vision of these killers.
"We are in touch with French officials and I have directed my Administration to provide any assistance needed to help bring these terrorists to justice."
Journalists' groups have expressed their outrage.
In a French-language statement, the union Syndicat National des Journalistes (SNJ) said: "There is no word strong enough to express the sadness and the anger of the profession today.
"The massacre perpetrated against the editorial staff of Charlie Hebdo is a horror that strikes at us all. When journalists are killed, it is done to make an entire profession feel fear; it is done to silence. Attacking a newspaper is an attempt to muzzle the freedom of expression that exists in a democracy."
The SNJ has called on newsrooms everywhere to observe a moment of silence, and for Parisians to rally this evening at Place de la Republique, not far from Charlie Hebdo's offices.
Donald Tusk, president of the European Council, said: "I am shocked by the appalling attack that took place this morning in Paris against Charlie Hebdo.
"The European Union stands side by side with France after this terrible act. It is a brutal attack against our fundamental values, against freedom of expression which is a pillar of our democracy.
"The fight against terrorism in all its forms must continue unabated.
"On behalf of the European Union and myself I extend my deepest condolences to the families and relatives of the victims and express my solidarity with the French authorities and the French people."
The novelist Salman Rushdie, who was threatened with death after the Islamic rulers of Iran said his book The Satanic Verses was blasphemous, said he stood with the magazine "against tyranny".
Rushdie, who lived under police guard for years after the book was published in 1988, said: "Religion, a mediaeval form of unreason, when combined with modern weaponry becomes a real threat to our freedoms.
"This religious totalitarianism has caused a deadly mutation in the heart of Islam and we see the tragic consequences in Paris today.
"I stand with Charlie Hebdo, as we all must, to defend the art of satire, which has always been a force for liberty and against tyranny, dishonesty and stupidity.
"'Respect for religion' has become a code phrase meaning 'fear of religion.' Religions, like all other ideas, deserve criticism, satire, and, yes, our fearless disrespect."
Communities Secretary Eric Pickles said: "All decent people mourn with France and share its determination to defend a free press."
Mr Clegg said in a statement: "My thoughts are with the victims of today's barbaric attack in Paris, and with their families and colleagues.
"Acts of terror like this will never ever shake our commitment to freedom of speech and civil liberties. It will never stop us from being a tolerant and liberal society.
"We will stick together and defy any attempts by radical extremists to gag or intimidate us. To the people of Paris I say, everyone in Britain stands with you in the aftermath of this vile attack."
Former Lib Dem leader Sir Menzies Campbell, a member of the Commons Foreign Affairs Committee, said media organisations may have to step up their security.
He said: "The depressing conclusion from these terrible events is that journalists exercising their right of free speech and expression may find themselves on the front line.
"Increased security for the media, as it is for example for air passengers and MPs, may be inevitable but we should regard these fundamental principles as inviolable."
Irish Taoiseach Enda Kenny joined the worldwide condemnation, saying he was shocked and appalled.
"Our thoughts are above all with the victims and their families, but also with the people of Paris and of France," he said.
"The murder of journalists and writers at their place of work is a direct attack on the basic values of freedom of speech and of tolerance. That this should have happened in a city and a country which for centuries have been leaders in the international struggle for human rights is a particular outrage.
"On behalf of the Irish Government, I offer our total solidarity and support to our French colleagues and friends as they work to capture the perpetrators and bring them to justice."
Shadow culture secretary Harriet Harman said the murders in Paris had "implications far beyond the tragic loss of those who died and beyond France".
Ms Harman warned: "There is a real concern that this crime will cause a chilling effect and undermine free speech.
"We have to be clear that the right of free speech is a basic human right for every individual and no democracy can function without freedom of the press...
"All political parties in this country will be clear on this and we should be prepared to take all the steps necessary to assure our journalists and media that we will do everything we can to defend that right of free speech and guard against the chilling effect or the self-censorship that these murders might engender."
Ms Harman added: "We must also guard against the danger that this murder will be used by Islamophobes or extremists to stir up religious and racial hatred. Muslims in this country - as The Muslim Council of Britain has said - will be horrified by this attack on free speech and loss of life.
"We must not allow free speech or our Muslim communities to be victims too in this terrible murder."
The European Newspaper Publishers' Association (ENPA) said it condemned the attack "in the strongest possible terms".
It said in a statement: "This atrocity is an attack on freedom of expression and press freedom, which is a core principle and pillar of European democracy.
"ENPA and all its members are appalled by this assault and remain united in the face of any threat to journalists and press publishers carrying out their daily role of informing citizens and fostering public debate.
"ENPA offers its profound sympathy to the families of the victims of this terrible attack. We express solidarity with our French member associations and with all French publishers and journalists for this dreadful loss of life.
"The attack on Charlie Hebdo underlines the necessity for all European decision-makers to defend strongly the principle of freedom of the press in both Europe and across the world."
Christine Lagarde, the managing director of the International Monetary Fund (IMF) and a former government minister in France, said: "My heart goes out to the victims' families and friends of this horrific and senseless act of barbarism. Charity must prevail."
The Archbishop of Canterbury Justin Welby said: "This is an act of the most extraordinary brutality and barbarity. This violence is demonic in its attack on the innocent, and cowardly in its denial of the basic human right of freedom of speech.
"The people of France, a country in which I have lived, which I know and love, will rise courageously above the challenge of this vile attack and continue to demonstrate strength and confidence arising out of their great history.
"Our prayers and thoughts are especially with those who have been killed and injured and their families. I pray also for those involved in pursuing the terrorists."
Ukip leader Nigel Farage said the the attack was "truly horrific" and had "some very worrying implications for our civilisation - free speech, satire, all things that Western countries believe in and love and have enjoyed for centuries".
He said there was a "fifth column" within Western societies and it should lead people to question multicultural policies.
He told Channel 4 News: "We see something like this happening; it's going to make many commentators in lots of spheres very nervous about poking fun or saying anything."
He added: "There is a very strong argument that says that what happened in Paris today is a result - and we've seen it in London too - is a result I'm afraid of now having a fifth column living within these countries.
"We've got people living within these countries, holding our passports, who hate us.
"Luckily their numbers are very, very small but it does make one question the whole really gross attempt that encouraged division within society that we have had in the past few decades in the name of multiculturalism."