The move follows the UK’s Brexit vote, which triggered a leadership contest in the Conservative government.
Heathrow and Gatwick airports have been vying with each other over building an extra runway.
Heathrow boss John Holland-Kaye said expansion “must be a key building block in the government’s Brexit plan”.
“It will allow British exporters to trade with all the growing markets of the world, strengthening Britain’s position as one of the great trading nations,” he said.
“And at a time of uncertainty, a £16bn privately funded infrastructure investment will create jobs and growth across the UK.”
Last July, the Airport Commission recommended Heathrow be expanded with a third runway – a 3,500-m runway north of the two existing ones – at an estimated cost of £18.6bn.
But in December, the government delayed its decision, saying further work on noise, pollution and compensation needed to be carried out.
On Monday, Gatwick Airport said the Brexit vote showed it was “clearer than ever that only Gatwick can deliver the new runway Britain needs”.
Conservative leadership contender Boris Johnson, a prominent member of the Leave campaign, consistently opposed Heathrow airport expansion while he was Mayor of London.
It is almost exactly a year since the Airports Commission, chaired by Sir Howard Davies, issued its report on expanding airport capacity in the UK, says BBC business correspondent Theo Leggett.
Three options were shortlisted – an extension of one of Heathrow’s existing runways, a new runway at Gatwick, or a third runway at Heathrow.
All three proposals remain on the table. However, the Davies Commission was unambiguous – it said that the best option was a third runway at Heathrow. And although the government postponed its final decision, it was widely expected to follow the Commission’s recommendation – until now.
There is no point endorsing Heathrow if the next prime minister were to overturn that decision, he says.
Our correspondent adds that the delay was good news for Gatwick, but bad news for the businesses that have been lobbying for a decision to be taken before the end of the summer.
Business campaign group London First said the deferral of the decision was “disappointing”.
“Nothing can be more vital for a trading island than sufficient air links, especially after the referendum result,” said London First chief executive Baroness Jo Valentine.
“There should be no question that whoever takes over from David Cameron must keep the government’s commitment to open a new runway by 2030.”
London First and Tesco chairman John Allan said the delay would be “a very serious setback, not just for London but for the whole country”.
