Justice Minister Michael Gove rocked Vote Leave co-leader Boris Johnson's expected bid to succeed Conservative Prime Minister David Cameron on Thursday by announcing his own candidacy for the British premiership.

"[Johnson] cannot provide the leadership for the task ahead," Gove said.

Gove and Johnson had cooperated closely in the successful Vote Leave 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.

Home Secretary Theresa May also announced her bid to lead the country on Thursday, saying she could provide "stability and certainty" and unify her divided party. Johnson was expected to speak to reporters by midday.

"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 and Andrea Leadsom, another prominent campaigner for Brexit, joined them on Thursday.

"Delighted to say I'm running for the Conservatives leadership," Leadsom said on Twitter. "Let's make the most of the Brexit opportunities!"

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

"Over the past week it has become clear just how divided our nation is - between young and old, north and south and those with different education and work backgrounds," Morgan said in her statement.

"So it is clear to me that the next leader of the Conservative Party must be someone who can unite the country," she said, adding that Gove is "the right person to do that."

Gove released a statement saying he had "repeatedly said that I do 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.

"I have, therefore, decided to put my name forward for the leadership."

Johnson and Home Secretary Theresa May remain the favourites to replace Cameron, while Gove is regarded as an outsider.

Nominations close 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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