Ruth Davidson has thrown her support behind Sajid Javid to become the next prime minister, saying he is "the man for the job".
The Home Secretary was described by Ms Davidson in an interview with the Mail on Sunday as someone whose life "embodies the Conservative values of aspiration, education, opportunity, hard work and just reward”.
The support of Ms Davidson, a popular figure in the party who has revitalised the Tories in Scotland, was welcomed by Mr Javid.
He told the Mail on Sunday: "Ruth knows a winner when she sees one.”
Mr Javid has outlined plans to set aside hundreds of millions of taxpayers' money to fund technology which could help solve the problem surrounding the Irish border.
He said: “I think it’s morally justified to pay for that because we both have signed the Good Friday Agreement, we are both absolutely committed to peace on the island of Ireland and – given that we voted to leave and that’s what’s changing the status quo on the island of Ireland – I think it’s morally right that we say, ‘look, we’ll pay because we’ve caused this’.”
However Communities Secretary James Brokenshire gave his backing to Boris Johnson, saying he has the “character, the ingenuity, the resilience and an ability to convey a compelling message”.
He told the Mail on Sunday that Mr Johnson will “drive an optimistic One Nation vision beyond Brexit on schools, hospitals, jobs and the economy, enabling greater prosperity and opportunity”.
Rory Stewart's team said he is the candidate best placed to beat Mr Johnson, citing an Opimium poll which shows him neck-and-neck with the former foreign secretary on the question of “would they make a good prime minister”.
An ally of the International Development Secretary said: “It’s clear – this polling shows Rory Stewart is the people’s candidate and is the ideal person to go up against Boris in the final two.”
Earlier, Dominic Raab said the possibility of suspending Parliament – possibly dragging the Queen into a constitutional row – should not be ruled out in order to secure Brexit.
The Tory leadership contender said it was “very unlikely” it would be necessary to prorogue Parliament in order to prevent MPs blocking a no-deal Brexit, but taking the option off the table would be a mistake.
Mr Raab said it was a “test of nerve” and his rivals would weaken the UK’s position in negotiations with Brussels by ruling out options to guarantee Brexit.
Critics of the approach have warned prorogation would involve the Queen in a constitutional crisis, because formally it is the monarch who ends a session of Parliament.
Bur Mr Raab said it is unlikely to come to that because MPs’ powers to block a no-deal Brexit are limited.
Pointing to Institute for Government analysis, he said it would be much more difficult “for Parliament to engage in the guerrilla warfare sabotage of a government” that was resolved to leave by October 31.
But in a message to his rivals – and an appeal to hardline Brexiteers on the Tory benches to back his campaign – Mr Raab said it is necessary to demonstrate a willingness to take such measures.
“I think it’s wrong to rule out any tool to make sure that we leave by the end of October,” he told BBC Radio 4’s Today.
“The exam question in this contest is ‘who can be trusted to lead us out by the end of October and end this paralysing uncertainty’.”
Mr Raab said he would go back to Brussels with a “best, final offer” including the removal of the Irish backstop, but said there could be no further delay and the UK would be prepared to leave without a deal, falling back on World Trade Organisation (WTO) rules.
“I think anyone who is talking about delay or who is taking WTO off the table is having the perverse effect of weakening our negotiating position in Brussels, that’s the lesson of the last three years,” he said.
“It’s a test of nerve here and if candidates cannot stand up their resolve to lead us out by the end of October in a leadership contest, what chance would they have under the heat of the negotiations in Brussels?”
Following Theresa May’s formal resignation as Tory leader on Friday, the starting gun has been fired for the race to replace her.
The nomination process will take place on Monday, with candidates requiring eight MPs to back them in order to enter the race, with the first round of voting on Thursday.