The co-leader of Britain's Vote Leave campaign, Boris Johnson, ruled himself out of the race to replace Prime Minister David Cameron on Thursday after his key Brexit ally questioned his leadership credentials and announced his own surprise candidacy.

Johnson, who had been one of the favourites to succeed Cameron, told reporters he had consulted Conservative colleagues about who should lead the party and the country. "I have concluded that person cannot be me," he said.

"My role will be to give every possible support to the next Conservative administration, make sure we properly fulfil the mandate of the people that was delivered at the referendum and to champion the agenda I believe in," Johnson said.

His announcement followed Justice Minister Michael Gove declaring his candidacy earlier Thursday and saying Johnson "cannot provide the leadership for the task ahead."

Gove and Johnson had cooperated closely in their successful campaign for a British EU exit, or Brexit, and many analysts had expected Gove to support Johnson's campaign to become the next Conservative leader.

Gove released a statement saying he had "repeatedly" said that he did not want to be prime minister.

"But events since [the referendum] last Thursday have weighed heavily with me," he said, adding that he had originally "wanted to help build a team behind Boris Johnson" to ensure the country had a pro-Brexit leader.

"But I have come, reluctantly, to the conclusion that Boris cannot provide the leadership or build the team for the task ahead," Gove said.

He was backed on Wednesday by media mogul Rupert Murdoch, who told The Times CEO Summit in London that Gove, a former journalist at the newspaper, was "the most principled and most able" candidate.

"He could run a fine government," said Murdoch, 85, who remains executive chairman of global media firm Newscorp, which owns The Sun and The Times in Britain.

However, Home Secretary Theresa May, who made her case on Thursday to unify the party and bring stability to the country, is now the bookmakers' favourite to succeed Cameron.

May told supporters and journalists that she could provide "stability and certainty."

"I think what the public want is strong, resilient leadership," said May, who backed Cameron's Remain campaign but kept a low profile in the final few weeks before the Brexit referendum.

May said there could be no backtracking on Brexit, and no general election until 2020, when the Conservative government's current term ends.

She said Britain should keep the benefits of the EU single market but "gain more control over the number of people coming here."

May promised to launch a "new and radical programme of social reform" to include "big changes to the way we think about our economy, our society and our democracy."

Health Secretary Jeremy Hunt said he would not be standing for the Conservative leadership and was backing May.

Welfare Secretary Stephen Crabb and former defence secretary Liam Fox declared their candidacy earlier. Andrea Leadsom, another prominent campaigner for Brexit, joined them on Thursday.

"I see a huge opportunity from the result of the referendum," Leadsom said in a video statement. "What we have to do now is to all pull together and make that oppotunity a reality."

Education Secretary Nicky Morgan meanwhile ruled herself out of the race, pledging support for Gove.

Nominations closed at midday Thursday (1100 GMT) and the Conservative Party has promised to complete the election process by September 9.

Cameron resigned on Friday, shortly after the final result of the Brexit referendum confirmed the failure of his campaign to persuade the public to remain in the EU.

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