The Government has restated its opposition to a third runway at Heathrow as a senior Tory challenged David Cameron to show if he was a "man or a mouse" by reversing the policy.

Writing in the Daily Telegraph newspaper, chairman of the Energy and Climate Change Committee Tim Yeo urged a U-turn on Heathrow policy, insisting expansion of Heathrow would give the Government "a sense of mission".

He said Mr Cameron risks "a dignified slide towards insignificance" with voters unable to see his priorities and passions, and that Heathrow is an opportunity to grasp the nettle. Mr Yeo later denied that he is "throwing down a gauntlet" to the Prime Minister.

In his article, Mr Yeo said: "Does he want to be another Harold Macmillan, presiding over a dignified slide towards insignificance? Or is there somewhere inside his heart - an organ that still remains impenetrable to most Britons - a trace of Thatcher, determined to reverse the direction of our ship? An immediate go-ahead for a third runway will symbolise the start of a new era, the moment the Cameron Government found its sense of mission. Let's go for it."

Downing Street said the coalition will stick to its commitment of having no third runway, with a spokeswoman for No 10 saying: "The coalition parties have made a pledge not to have a third runway and that is a pledge that we will keep. We don't see the argument for a third runway."

Transport Secretary Justine Greening admitted on the BBC Radio 4 Today programme that it would be difficult for her to remain in post if the Government changed its mind on a third runway: "But I think, at the end of the day, the process I'm about to kick off is one that will see us come up with a much better, longer-term solution."

The planned runway was opposed by both the Tories and Liberal Democrats at the general election and the coalition agreement between the two parties explicitly cancelled the expansion. Conservative London Mayor Boris Johnson also opposes a third runway at Heathrow, favouring instead a new airport in the Thames Estuary to the east of the capital.

Speaking later, Mr Yeo insisted he is not "throwing down a gauntlet" to Mr Cameron, but told the BBC: "I am saying there is a terrific opportunity for him to show really strong leadership from the front and to set out something which is not clear to everyone yet: what his vision of Britain is going to be in 2020."

Deputy Prime Minister Nick Clegg, on a visit to North Tyneside, said there was no chance of a U-turn: "We're not going to give the go-ahead to the third runway at Heathrow because we said very clearly as both parties that we wouldn't do so, so we're going to stick to the coalition agreement.

"But that doesn't mean we're going to stick our heads in the sand over the aviation debate about capacity in this country, and how do we make sure we have those proper connections to economies in Asia and Latin America which are important to our own prosperity. And we'll make sure we look at that. But there are lots of ways of doing that and we shouldn't just lurch to one solution because one individual MP was to say so."