Justice Secretary Michael Gove and Home Secretary Theresa May lead a five-way race to be the next Conservative Party leader and UK prime minister.
Mr Gove was a surprise addition to the race, having been expected to back Boris Johnson, who shocked the political world by ruling himself out.
Minister Andrea Leadsom, MP Liam Fox and Work and Pensions Secretary Stephen Crabb are also in the running.
The winner of the contest is set to be announced on 9 September.
The leadership battle has been sparked by David Cameron's decision to step down as prime minister after losing the EU referendum, which saw the country vote by 52% to 48% to leave the EU.
Mr Gove's announcement early on Thursday that he would challenge the leadership was unexpected, as the justice secretary had been expected to throw his weight behind fellow leading Leave campaigner Mr Johnson for Conservative leader.
Explaining his decision, he said: "I have repeatedly said that I do not want to be prime minister. That has always been my view. But events since last Thursday have weighed heavily with me.
"I respect and admire all the candidates running for the leadership. In particular, I wanted to help build a team behind Boris Johnson so that a politician who argued for leaving the European Union could lead us to a better future.
"But I have come, reluctantly, to the conclusion that Boris cannot provide the leadership or build the team for the task ahead."
By Ben Wright, BBC political correspondent
"Shakespearian" is the word being mumbled by dazed politicians and pundits at Westminster.
The ambitions, rivalries and duplicitous double-dealing unleashed before the Tory leadership contest even got underway has left onlookers groping for fictional comparisons.
It's Richard III meets Scarface, with a bit of Godfather thrown in.
Remember this: David Cameron, Boris Johnson, Michael Gove and George Osborne grew up together - personally and politically. Their families were close. But the EU referendum ripped through old loyalties.
First Michael Gove backed the Leave campaign, knowing the damage it could do to Cameron and Osborne. The chancellor and Gove kept their friendship intact despite the strain of the campaign.
But it was Boris Johnson's decision to lead the Leave campaign and put his own ambitions to be prime minister ahead of loyalty to David Cameron that severed his relationship with the now departing PM, destroyed by Leave's victory.
Boris Johnson believed the crown would be his and naively believed Michael Gove's promises of support. But now Mr Gove, despite polite protestations he never coveted the top job, has ruthlessly dispatched his friend.
What has been going on behind the scenes? The truth will only emerge in memoirs.
But my sense is Mr Gove and his team of advisors clearly did not believe Boris Johnson had the spine to fully divorce Britain from the EU. Nor did a number of Tory Mps trust Mr Johnson to deliver the promises he was making in terms of personnel and jobs.
When Mr Gove made his move, hardened Brexit believers instantly went with him, sinking Boris Johnson.
The irony of course is that Boris Johnson, who did so much to take Britain out of the EU, has seen his own ambitious crushed in the aftermath.
It could be that the big winner from this vicious Tory drama is the woman in charge of law and order - Theresa May.
Setting out his pitch for the leadership, the cabinet minister - best known as a controversial education secretary before becoming one of the faces of the Leave campaign - said: "I want there to be an open and positive debate about the path the country will now take.
"Whatever the verdict of that debate I will respect it. In the next few days I will lay out my plan for the United Kingdom which I hope can provide unity and change."
Conservative MP David Davis told BBC Radio 5 Live Mr Gove's decision must have been taken "very late", as Mr Gove's assistant had asked him on Wednesday night to attend Mr Johnson's campaign launch on Thursday.
Justice minister and Leave campaigner Dominic Raab, who switched his support from Mr Johnson to Mr Gove, told the BBC's Daily Politics that "Boris was cavalier with assurances he made" and had failed to put together a "strong unifying team".
Who's in the running?
Home Secretary Theresa May: The 59-year-old has overtaken Boris Johnson as the bookies' favourite to win the contest. She's held the Home Office brief - often something of a poisoned chalice - since 2010, and is a former Tory party chairman. She says she can offer the "strong leadership" and unity the UK needs, and promised a "positive vision" for the country's future. She backed staying in the EU.
Justice Secretary Michael Gove: The 48-year-old former newspaper columnist was a key figure in the party's modernisation that led to its return to power in 2010. He was a reforming, if controversial, education secretary between 2010 and 2014, and now holds the Ministry of Justice brief. He was a leading player in the Brexit campaign - which put a strain on his close friendship with David Cameron. He has pitched himself as the candidate that can provide "unity and change."
Work and Pensions Secretary Stephen Crabb: The 43-year-old was promoted to the cabinet in 2014 as Welsh secretary, and boosted his profile earlier this year when he took over as work and pensions secretary. A rising star of the Tory party he has promised to unite the party and country following the referendum result and provide stability. Raised on a council estate by a single mother, he has a back story to which many Tory MPs are attracted. Backed Remain.
Energy minister Andrea Leadsom: The 53-year-old former banker and fund manager was one of the stars of the Leave campaign. A former district councillor, she became MP for South Northamptonshire in 2010 and - after serving as a junior Treasury minister and as a member of the Treasury select committee - she was made a junior minister in the energy and climate change department in May last year.
Former cabinet minister Liam Fox: It's second time around for the 54-year-old ex-defence secretary and GP, who came a close third in the 2005 leadership contest. His cabinet career was cut short in 2011 when he resigned following a lobbying row. A Brexit campaigner, and on the right of the party, he has said whoever becomes PM must accept "the instruction" of the British people and not "try to backslide" over EU membership.
Launching her leadership bid in central London, Mrs May - one of the longest-serving home secretaries in history - said the UK needed "strong proven leadership to steer us through this period of economic and political uncertainty and to negotiate the best possible terms as we leave the European Union".
She also pitched herself as the candidate that could "unite our party and our country" and offer "a bold, new positive vision" for the country's future that "works not for a privileged few, but for every one of us".
Although Mrs May - the daughter of a vicar - backed Remain she maintained a low profile during the campaign and, in her speech, insisted she would not back away from last week's vote. "Brexit is Brexit."
But she said Article 50 - the formal mechanism for leaving the EU - should not be triggered until the UK had agreed its negotiating strategy - probably before the end of year.
She set out plans for a new government department to oversee the UK's withdrawal from the EU - and said it would be headed by a pro-Brexit cabinet-level minister.
And she said she would, as prime minister, abandon plans to pull Britain out of the European Convention on Human Rights, saying she did not expect there to be a parliamentary majority for it.
Mrs May acknowledged she was "not a showy politician", adding: "I just get on with the job in front of me" - suggesting that was what the country wanted.
Former Defence Secretary Liam Fox, meanwhile, said any Brexit deal which included free movement of people would be "a betrayal" of the referendum result, as he kicked off his campaign.
He said free movement was a political preference which needed to challenged. And he said the UK should approach the post-EU era with "confidence".
Energy minister Andrea Leadsom, who also announced her candidacy on Thursday, told the BBC that delivering Brexit was an "absolutely top priority" for the next prime minister.
"It's not just about leaving something, it's about re-engaging with the rest of the world," she said.
She also said she had a "real desire to see the social justice in our country turned around" and said her focus, if elected, would be on mental health, improving skills and getting young people into work.
Work and Pensions Secretary Stephen Crabb, who was the first to launch his leadership bid and who campaigned to stay in the EU, vowed to make curbing immigration a "red line" in Brexit negotiations - and he ruled out a snap general election and a second EU referendum.
The former Welsh secretary said stability was his aim. He also pledged to confront economic and social divisions across the UK, build a strong economy and improve trade links, if he won the contest.
Speaking before Mr Johnson's decision to pull out Mrs May joked: "Boris negotiated in Europe. I seem to remember last time he did a deal with the Germans, he came back with three nearly-new water cannon."
The then London mayor purchased the riot control water cannon following the riots in the capital city in 2011 - but Mrs May eventually withheld permission for their use.
In a speech that had been billed as his campaign launch on Thursday, Mr Johnson, who has long harboured ambitions to be leader and prime minister, announced he would not be standing.
Mr Johnson said the next Conservative leader would have to unify his party and ensure that Britain stood tall in the world.
"Having consulted colleagues and in view of the circumstances in Parliament, I have concluded that person cannot be me," he said, just moments before the noon deadline passed.