Michael Gove has insisted he has "evolved" as a politician since previously stating he was "incapable" of being prime minister.
The environment secretary and prominent Brexiteer said he was putting his name forward "to be prime minister of this country" as he became the eighth MP to launch a formal bid to succeed Theresa May.
His announcement came as rival candidates Esther McVey and Dominic Raab said the UK should leave the EU on 31 October with or without a deal - a message echoed by fellow contenders Boris Johnson and Andrea Leadsom.
Mr Gove, who ran for the leadership in the 2016 election, claims he has gained more experience since remarking he was incapable of being PM.
"In those three years I have been through a variety of experiences," he told BBC Radio 4 podcast, Political Thinking with Nick Robinson.
"I led, some people may lament this, but I lead the campaign to leave the European Union and that involved going up head to head with David Cameron and others in the debate formats that we had.
"And being tested during that campaign, having had time to reflect when I was on the backbenches and then coming back into government.
"I think that I've evolved as a politician, but, obviously, we'll see in the course of the next few days and weeks who people think has what it takes."
Chancellor Philip Hammond, who is not running himself, has warned it would be a "dangerous strategy" to ignore parliament, which has opposed no-deal.
He also refused to rule out supporting a no confidence motion in the government if the next Tory leader goes for a no-deal Brexit.
Ms McVey, the former work and pensions secretary, told Sky's Sophy Ridge on Sunday that the UK must start preparing for a no-deal exit straight away.
"We won't be asking for any more extensions," she said.
"If Europe wants to come back to us, the door is open if they want a better deal. Time is limited, we have to make sure we are ready to leave."
Ms McVey also claimed there would be no hard border on the island of Ireland under a no-deal Brexit, saying it would be "invisible".
"There will be an invisible border, the technology already exists to be able to put that in place," she added.
However, a Home Office document leaked last month suggested that any such technical solution could be more than a decade away.
Mr Raab said he would keep a no-deal Brexit on the table while he tries to negotiate a better settlement with the EU, claiming negotiations need to be more resolute than before.
"It is achievable, but it will need some good will on the other side too," the former Brexit secretary told the BBC's Andrew Marr Show.
Mr Raab initially failed to rule out working with Nigel Farage's Brexit Party, saying he listened to "all sides of this debate".
He later issued a statement clarifying his stance and insisted he would "not do an electoral pact" with Mr Farage if elected Tory leader.
Labour's shadow chancellor John McDonnell told Sky's Sophy Ridge on Sunday that there was "a real threat now of an extremist Brexiteer becoming the leader of Conservative Party and taking us over the cliff edge of a no deal".
Mr Hammond told the Andrew Marr Show it would be "very difficult" for a prime minister who adopted no-deal as a policy to retain the confidence of the House of Commons.
Asked if whether he would vote against the government on a no-deal withdrawal if he was a backbencher in the autumn, the chancellor said: "I would certainly not support a strategy to take us out with no deal."
He declined to say whether he would vote against the government in a confidence motion in the circumstance of no deal, saying it was "a hypothetical question".
Tory leadership candidate Rory Stewart told Sky News that supporters of a no-deal Brexit are "deluding themselves or deluding the country".
"Anyone who thinks they can ride off to Brussels and get a new withdrawal agreement before October is either deluding themselves or deluding the country," the international development secretary said.
It came as former education secretary Justine Greening ruled herself out of the Tory leadership race, branding it a "beauty parade for hard Brexiteers".
She told Sky's Sophy Ridge on Sunday that the contest was a "narrow discussion in a narrow Conservative Party that's really around what version of hard Brexit to do".
Meanwhile, former first secretary of state Damian Green backed Health Secretary Matt Hancock to succeed Mrs May as Tory leader.
Mr Green told Sky's Sophy Ridge that the Conservative Party needs someone who can "speak the language of those who grew up in the digital world".
Mrs May announced on Friday she will resign as Conservative Party leader on 7 June, with a new Tory leader set to take over as prime minister at the end of July.
The timetable for the contest will see nominations close in the week of 10 June and MPs involved in a series of votes to whittle down the crowded field to a final two contenders.
Tory party members will then decide who wins the run-off.