The expansion timetable set out by the Airports Commission might be met only if incoming prime minister Theresa May makes a decision on which project to back by October, Transport Secretary Patrick McLoughlin has warned.
The commission, chaired by Sir Howard Davies, published its final report in July last year stating that a new runway was needed in south-east England by 2030 and recommending that Heathrow's plan should go ahead.
But in December the Department for Transport announced that further investigation into noise, pollution and compensation was needed and last month Mr McLoughlin said the decision had been deferred until "at least October" following David Cameron's resignation.
In an interview with the Press Association, the Transport Secretary stressed the importance of the decision being made as soon as possible.
Mr McLoughlin said: "So long as we can get a decision as quickly as we can in October, we can still stick to the timetable that was set out in Davies."
The timing of the decision was "a case for the Prime Minister", he said, adding: "Parliament rises next week so in all honesty I still think we're probably looking at around about the October period.
"I don't think this is a decision that could be made when Parliament is not sitting."
Mr Cameron was expected to confirm whether projects at Heathrow or Gatwick would be supported shortly after the EU referendum, but the victory for the Leave campaign means the decision has been left for successor Mrs May.
Business leaders have criticised the delay, with the British Chambers of Commerce claiming the Government was "missing a golden opportunity to stimulate business confidence".
Mrs May's constituency, Maidenhead, is near the Heathrow flight path and she has previously raised concerns about noise and the environmental impact of a third runway at the airport.
In December 2008 she pledged to put pressure on Gordon Brown's government over proposals for expansion following the introduction of the Climate Change Act, which committed the UK to cutting carbon emissions.
She said: "I will continue to put pressure on the government over the third runway at Heathrow as an extra 222,000 flights a year would undermine our national targets and seriously damage the health of the local community."
During a meeting with Sir Howard in April 2014, Mrs May expressed the concerns that many local residents have about aircraft noise, particularly at night time, according to an article on her website.
But she also told him that a number of jobs in the Maidenhead area depend on Heathrow, with many of her constituents working at the airport.
She said: "The future of Heathrow Airport is of vital importance to the Maidenhead area - for local businesses who rely on good transport links, and for local residents concerned about noise and the environment."
Putney MP Justine Greening, who is a strong opponent of Heathrow expansion, has been tipped to return to the Cabinet under Mrs May.