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Liz Truss has said she would not make "disparaging comments" about her Tory leadership rivals amid claims the contest has turned nasty.
It comes as Penny Mordaunt - one of the contenders in the race to Number 10 - was criticised by a former minister.
Ms Truss and Ms Mordaunt are vying to become the main challenger to ex-chancellor and frontrunner Rishi Sunak.
Tory MPs will whittle down the field to a final two contenders, before Tory members vote on the winner.
Kemi Badenoch, Suella Braverman and Tom Tugendhat complete the field of candidates heading into the second round, the results of which will be announced shortly.
Former minister Lord Frost launched a stinging attack on Ms Mordaunt's record in government, saying he would have "grave reservations" about her becoming PM.
The Tory peer - who served as Boris Johnson's Brexit minister until he resigned last December - said he had asked Mr Johnson to "move her on" from a job as his deputy in talks with the EU.
Speaking to TalkTV, he added: "I felt she did not master the detail that was necessary in the negotiations last year. She wouldn't always deliver tough messages to the European Union when that was necessary.
"She wasn't always fully accountable, she wasn't always visible, sometimes I didn't even know where she was," he added.
The remarks were seized on by a supporter of Ms Truss, with Treasury Chief Secretary Simon Clarke saying: "Lord Frost's warning is a really serious one. Conservatives - and far more importantly our country - need a leader who is tested and ready."
Questioned about the remarks at an event to launch her campaign, Ms Truss replied: "I certainly won't be making any disparaging comments about any of my fellow candidates.
"In fact, the Conservative race shows what a broad range of talent we have in the Conservative Party."
A source in the Mordaunt campaign said she had "nothing but respect" for Lord Frost, who "did a huge amount to assist our negotiations until he resigned from government".
"Penny will always fight for Brexit and always has," they added.
Ms Truss was also asked about a report in the Times quoting an ally of hers saying now was not the time for a prime minister who needed "stabilisers", an apparent dig at Ms Mordaunt's more junior position in government.
In reply, Ms Truss said she was "putting forward a positive agenda" and if elected wanted have put in place "a team from across the Conservative Party, getting all of our talents on the pitch to be able to do that".
The same report also quoted an ally of Ms Mordaunt accusing Ms Truss of running a "dog-whistle, anti-woke Faragist campaign".
The comments are the latest war of words between rival camps, as the leadership debate becomes increasingly acrimonious.
On Wednesday, Ms Badenoch had a feisty exchange with Culture Secretary Nadine Dorries, a Truss backer, over a delay to new internet safety laws that Ms Dorries has been trying to pilot through Parliament.
Former minister Mrs Badenoch tweeted that the bill was "in no fit state to become law" adding that "we should not be legislating for hurt feelings", prompting Ms Dorries to reply: "Which part of the bill legislates for hurt feelings, Kemi?"
However, Mrs Badenoch did not respond so curtly to one of her rivals in the contest. In a tweet including a picture of Mrs Badenoch and Suella Braverman together, both posing in blue dresses, Mrs Badenoch said "this is the only blue on blue you'll be seeing from me and Suella Braverman during this campaign".
Mr Sunak's operation was not exempted from accusations of briefing against rivals, and on the BBC's Today programme he was asked about the role of former chief whip Sir Gavin Williamson as part of his campaign.
Mr Sunak said: "Like all the Members of Parliament who are on my team, they are talking to colleagues and making the case for my candidacy because they believe that I am the best person to beat Keir Starmer and the Labour Party and I'm really grateful for all their support."