Dominic Raab has become the latest Conservative MP to say he will run for Tory leadership.
The former Brexit secretary is the sixth Tory to enter the race after Theresa May said she would resign as party leader on 7 June.
Speaking to the Mail on Sunday, Mr Raab said he would prefer for the UK to leave the EU with a deal.
But he said the UK must “calmly demonstrate unflinching resolve to leave in October – at the latest”.
Whoever wins the leadership contest will become the UK’s next prime minister.
Party bosses expect a new leader to be chosen by the end of July.
Mrs May will continue as prime minister while the leadership contest takes place.
She agreed with chairman of the Tory backbench 1922 Committee, Sir Graham Brady, that the process to choose a new leader should begin the week after she stands down.
Five other candidates have, so far, confirmed their intention to stand:
- Foreign Secretary Jeremy Hunt
- International Development Secretary Rory Stewart
- Health Secretary Matt Hancock
- Former Foreign Secretary Boris Johnson
- Former Work and Pensions Secretary Esther McVey
Earlier, other Conservative leadership contenders clashed over Brexit.
Mr Hancock said Mrs May’s successor must be more “brutally honest” about the “trade-offs” required to get a deal through Parliament.
And Mr Stewart said he would not serve under rival Boris Johnson because of his backing for a no-deal exit.
In the Mail on Sunday article, Mr Raab – who voted for Brexit in the 2016 referendum – said: “We can’t live in a country where politicians make promises to respect your vote in a referendum, and then junk them if they don’t like the verdict.
“The country now feels stuck in the mud, humiliated by Brussels and incapable of finding a way forward. The prime minister has announced her resignation. It’s time for a new direction.”
Mr Raab said “leadership with conviction” was needed to change the dynamic of Brexit.
He added: “I will fight for a fairer deal on Brexit, a fairer deal for British workers, and a fairer society where every child can fulfil their potential.”
He was the second Brexit secretary to resign, in November 2018.
At the time he said he quit the cabinet over “fatal flaws” in the draft Brexit agreement with the EU.
Who are the Conservative members?
Most members of most parties in the UK are pretty middle-class. But Conservative Party members are the most middle-class of all: 86% fall into the ABC1 category.
Around a quarter of them are, or were, self-employed and nearly half of them work, or used to, in the private sector.
Nearly four out of 10 put their annual income at over £30,000, and one in 20 put it at over £100,000. As such, Tory members are considerably better-off than most voters.
Tory MPs have until the week commencing 10 June to put their name forward, and any of them can stand – as long as they have the backing of two parliamentary colleagues.
The candidates will be whittled down until two remain, and in July all party members will vote to decide on the winner.
The Conservative Party had 124,000 members, as of March last year. The last leader elected by the membership was David Cameron in 2005, as Theresa May was unopposed in 2016.
It will be the first time Conservative members have directly elected a prime minister, as opposed to a leader of the opposition.