Nicky Morgan has backed Michael Gove in the Tory leadership race.
Mr Gove made a surprise announcement on Thursday morning that he is putting himself forward to succeed David Cameron, saying he does not believe Boris Johnson can "provide the leadership or build the team for the task ahead".
In a statement, the Education Secretary said she has "concluded unequivocally" that Mr Gove has the "skill and credibility to put together the right team to renegotiate our exit from and future relationship with Europe, and explain the final terms to the British people."
Jeremy Hunt will not be standing for the Tory leadership, saying "now is not the right time".
In a statement, the Health Secretary gave his support to Theresa May.
I have decided that now is not the right time for me to run for the leadership - though I remain completely committed to ensuring we secure our position as a great trading nation with sensible controls on migration.
I believe that Theresa May has the strength, judgement and values to deliver those things. She is the right choice to lead Britain in a challenging period and will make a truly outstanding Prime Minister.
ITV News Political Editor Robert Peston has likened the Conservative leadership campaign to being "like the last days of Rome".
In a video uploaded to his Facebook page, he added: "It's going to be an extraordinary contest. Just when you thought it couldn't get any madder, it certainly has."
Boris Johnson has decided to continue with his leadership bid, amid speculation that he was considering withdrawing from the contest.
So @borisjohnson has decided not to pull out of contest. Leave vote split between him and Gove and Fox. May looking strongest
Theresa May has launched her bid to become the next leader of the Conservative Party.Read the full story ›
Andrea Leadsom has announced she is running for the Conservative Party leadership.
On Thursday morning, she tweeted: "Let's make the most of the Brexit opportunities!"
She earlier commented the Brexit result was a "huge opportunity for our great country".
Michael Gove is to stand for the Conservative Party leadership, saying he does not believe Boris Johnson can "provide the leadership".Read the full story ›
A Tory MP who backed the Remain campaign would find it "much harder" to have the "credibility" needed to become the party's new leader and prime minister, Dr Liam Fox has said.
The former Defence Secretary, who backed Leave, said it would not be "impossible" for a Remain campaigner to succeed David Cameron, but Leave campaigners have a "natural credibility".
Dr Fox is to stand as a candidate for the Conservative party leadership, with Stephen Crabb, Boris Johnson and Theresa May also in the running.
Speaking on ITV's Good Morning Britain, Dr Fox refused to say who he would back if he is not successful.
"I'm a very good friend of Stephen Crabb, I had great fun campaigning with Boris Johnson on the winning side, I had great experience working with Theresa May in government on national security. I respect all of them," he said.
"I think it's much harder for anybody who voted for remain to have the credibility amongst the voters who voted to leave in terms of leading the country. It's not impossible, but it's much harder. That's why I think for those of us who were on that Leave side there is a natural credibility with the voters."
Conservative heavyweights Boris Johnson and Theresa May are to launch their leadership bids on Thursday.Read the full story ›