Transport Secretary Chris Grayling has insisted the Government is not in danger of toppling and will see out a full term.
Responding to claims by Jeremy Corbyn that Labour could be in power within a year, Mr Grayling said no Tory MP would want to trigger an early election.
He told BBC Two's Newsnight: "I think that's a sign of why Jeremy Corbyn isn't fit to be prime minister. He obviously hasn't read the Fixed Term Parliaments Act. The next general election is due in June 2022.
"It is not at all a Government that is going to topple. We have got a strong relationship with the DUP. We have got a team of Conservative MPs who are committed to taking this country forward.
"When people say this, I ask the question 'can you name the Conservative MP who is going to vote for an early election, who is going to abandon the Brexit process and leave the country in danger of a far left-wing government led by Jeremy Corbyn?'
"There is no such member of parliament."
Mr Grayling also accused Labour-supporting groups such as Momentum of bringing a "nastiness" into politics.
Tory MP George Freeman, former chairman of the Prime Minister's policy board, warned that getting Brexit wrong could be a "catastrophe" for conservatism.
He told the BBC: "It is really urgent, that as the Prime Minister sees through the noble and, frankly, thankless task of negotiating Brexit that under her leadership a messianic piece of work has begun, to make this a moment of Conservative renewal that can inspire those who didn't vote for it.
"I think it's very urgent. I think if we don't, this is in danger of being a Brexit that breaks, not makes conservatism. We are in a risk of this being a moment, a catastrophic moment, where conservatism isn't forgiven by a generation that didn't vote for it."