Michael Gove and Andrea Leadsom have emphasised the need for the next prime minister to have backed Leave in the EU referendum as they made pitches to become the next Conservative leader.
Mr Gove told the Sunday Telegraph the next leader needed to have “embraced the vision of independence”.
Mrs Leadsom told the paper it would be difficult for someone who voted Remain to see the “opportunities” of Brexit.
But Theresa May said the government “cannot just be consumed by Brexit”.
The home secretary, who campaigned to remain in the EU, has become the favourite to become the next leader after Boris Johnson pulled out of the contest.
As of 18:00 BST on Friday, Mrs May had secured the backing of 96 Tory MPs, while Stephen Crabb had 22, Mrs Leadsom had 21, Mr Gove had 18 and Liam Fox had 10.
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In an interview with the Sunday Telegraph, Mrs Leadsom said Mrs May should not become the next prime minister because she did not believe in Brexit.
“I think it’s very difficult for somebody who doesn’t agree with that, who is reluctantly following the wishes of the people. I think it’s quite hard for them to really see the opportunities.
“I genuinely believe that if we want to make a go of it then we need somebody who believes in it.”
The energy minister also said she wanted to emulate the leadership qualities of Lady Thatcher, who was Conservative prime minister from 1979 to 1990.
She said: “As a person, she was always kind and courteous and as a leader she was steely and determined.
“I think that’s an ideal combination – and I do like to think that’s where I am.”
‘My confidence evaporated’
The contest to become leader of the Conservative Party follows Prime Minister David Cameron’s announcement he would stand down by the autumn after the UK voted to leave the EU in the 23 June referendum.
Whoever is elected Conservative leader will succeed Mr Cameron as prime minister and be responsible for negotiating the UK’s exit from the EU.
Mr Gove, writing in the Sunday Telegraph, also said the next prime minister should be someone who had campaigned for Brexit.
“It is clear to me that the prime minister who takes charge of that process must be someone who embraced this vision of independence during the referendum,” the justice secretary said.
“I also believe personally that the new prime minister should have experience at the top level of government and a track record of delivering change.”
Mr Gove also explained how his confidence in Boris Johnson – a leading Brexit campaigner who had initially been regarded as the favourite to replace Mr Cameron – had “evaporated”.
He wrote: “Over the past week, to my deep regret, my confidence evaporated.
“That led me to make the difficult decision, at no little cost, to put friendships aside and act in the national interest.
“Having declared that I didn’t want to be prime minister – so often that I might as well have engraved it on my business card – I came to the uncomfortable conclusion that I was the person best qualified to deliver that change.”
‘Consumed by Brexit’
Former defence secretary Mr Fox, who also campaigned for Leave, also spoke to the Sunday Telegraph and said he would increase defence spending if he became leader of the party.
Meanwhile, in an interview with the Mail on Sunday, Mrs May rejected the suggestion the next leader needed to have backed Brexit.
“The government cannot just be consumed by Brexit, there is so much more to do,” she said.
More than 160 Conservative MPs have yet to declare whom they will support in the leadership contest.
The candidates will take part in a series of ballots of the party’s 330 MPs, starting on Tuesday.
The two most popular will then go on to a vote of the wider party membership, with the result due on 9 September.
Who’s backing who?
Who’s in the running?
Home Secretary Theresa May: The 59-year-old has replaced 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. Theresa May profile
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”. Michael Gove profile
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. Stephen Crabb profile
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. Andrea Leadsom profile
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. Liam Fox profile