A decision on airport expansion in south-eastern England is to be delayed until "at least October", Transport Secretary Patrick McLoughlin has said.
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."
But Gatwick Airport chief executive Stewart Wingate said: "The enormous pollution [of] both noise and air quality that Heathrow inflicts on hundreds of thousands of people, if not millions, it's this issue that politicians are going to have to grapple with."
"If you look at Gatwick, we have a tiny fraction of the environmental impact of Heathrow, yet you get all of the same economic benefits, all of the same connections to short haul and long haul destinations, all at a cheaper price."
Gatwick will press its case with the new leader of the Conservatives, he added.
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".
Analysis: Richard Westcott, BBC transport correspondent
Earlier today, the proposal to expand Heathrow took a major blow when the government deferred an airports decision to its next leader.
Boris Johnson was a front runner for the job and he's very hostile to the scheme.
But now he's stepped out of the race, things have become much less clear.
Theresa May and Michael Gove both have constituencies near Heathrow and they've both had to deal with a lot of noise complaints, especially when an experimental new flight path upset a lot of residents a couple of years ago.
But neither has ever come out against building a third runway at the airport and it's not clear what they think now.
And all of that's assuming one of them becomes leader.
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,
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.
Business campaign group London First said the deferral of the decision was "a huge shame".
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".
"There's clearly going to be a significant downturn in inward investment over the next few years until there's greater certainty," he told the BBC.
"Carefully judged infrastructure investment would be one way of filling that gap, and also a way of making a statement that the UK is open for business.
"We do want connectivity with the rest of the world, so I think it's a great shame that politicians are putting party interests before the national interest," Mr Allan added.
Paul Wait, chief executive of travel management industry body the GTMC, said: "Current political instability is jeopardising economic growth in many ways.
"For uncertainty on airport expansion to also be caught up in the shifting sands is both short-sighted and dangerous.
"Regardless of political beliefs, every UK business is crying out for messages of confidence and room to find new growth, including outside of Europe.
"Without greater airport capacity, and soon, UK businesses will be collateral damage in the circus that is currently unfolding."