Rival Tory leadership candidates have turned their fire on Penny Mordaunt as she continues to gather momentum in an increasingly acrimonious race. Rishi Sunak, the former chancellor, is still the frontrunner, having secured 13 more votes in the second-round ballot on Thursday than he had the previous day, and Mordaunt pulled away from the foreign secretary, Liz Truss, who added fewer MPs to her tally despite her high-profile launch earlier in the day. Suella Braverman, the attorney general, was knocked out of the race after receiving 27 votes in the second round, and immediately assailed Mordaunt over the issue of trans rights and later announced she would be backing Truss’s bid, along with the senior backbench MP Steve Baker, who ran her campaign. She criticised Mordaunt’s handling of legislation granting maternity leave to ministers last year – which Braverman had been the first to take up. “Penny Mordaunt, as the bill minister, the minister responsible for passing the bill, did oppose and did resist the inclusion of the word woman, and the inclusion of the word mother,” Braverman said. “I was quite disappointed by the way it was handled, and the responsible minister, I’m afraid, didn’t stand up for women.” Rival camps were sharing a video of Mordaunt discussing the legislation in the Commons at the time, in which she says: “Let me say in proposing, from this dispatch box, that trans men are men, trans women are women.” She adds that “great care” was taken in drafting amendments to reflect that. Since launching her campaign Mordaunt has sought to play down the idea that she is too “woke” for the tastes of Tory members. Meanwhile, Truss’s backers, including the former Brexit negotiator David Frost, and the chief secretary to the Treasury, Simon Clarke, raised questions publicly about Mordaunt’s performance as a minister. Lord Frost, referring to Mordaunt when she was in effect his deputy during the Brexit talks, told TalkTV: “I’m sorry to say this: she did not master the necessary detail in the negotiations last year. She wouldn’t always deliver tough messages to the EU when that was necessary, and I’m afraid she wasn’t fully accountable or always visible. Sometimes I didn’t even know where she was.” Clarke, who chose to back Truss in preference to his boss, Sunak, said: “It is telling, I think, where current members of the government are placing their support. That is reflected in a number of very senior ministers’ decisions about who to support in this race – they are not backing Ms Mordaunt.” Another Truss supporter, the former Tory leader Iain Duncan Smith, suggested the race was “going to get just a little bit personal”, adding: “I really genuinely don’t know what Penny has done in the last two and a half years apart from knowing the odd job title that she’s been in.” Mordaunt’s supporters said the ferocity of attacks on her underlined the way she had shaken up the race. “We’re taking on two establishments – the economic establishment and the Boris establishment,” one MP said. At her campaign launch, Truss sought to portray herself as a candidate for change, despite having the backing of the Boris Johnson super-loyalists Nadine Dorries and Jacob Rees-Mogg. “I can lead, I can make tough decisions and I can get things done,” Truss told a carefully choreographed event in Westminster, attended by her MP and cabinet backers. “I am ready to be prime minister from day one.” Sunak secured 101 votes in the second ballot of MPs, followed by Mordaunt, with 83, and Truss on 64. Kemi Badenoch, the former equalities minister, and Tom Tugendhat also made it through the latest round, though the latter lost five supporters. Tugendhat, the chair of the foreign affairs select committee, said he would continue his campaign and take part in the televised debates starting on Friday. At a press conference earlier in the day, Tugendhat acknowledged he was being courted so intensely by other camps hoping he would fold his campaign and join them that he felt “like a prom queen”. “I’m still in this fight,” he said. “What members of parliament and what members of the Conservative party need to know is that whoever it is they choose as the leader in this process is somebody who can champion those ideas and values in the election that’s coming in 2024. And then, I hope, maybe 2029 as well.” He said the race had been “a hell of a job interview”, but in an hour-long Q&A session with reporters the MP set out plans for green growth, a commitment to look at the universal credit taper rate to ease the cost of living crisis, and a boost to defence spending and army numbers. The chair of the foreign affairs select committee told LBC Radio that he did not think the privatisation of Channel 4 was a good idea, and said he would not scrap the BBC licence fee. Some MPs expect Tugendhat to withdraw before the third ballot on Monday afternoon, unless he believes his performance in the TV debates on Friday and Sunday has somehow catapulted him into contention. There will be final rounds of voting next week to narrow the choice to two candidates. The Conservative party members will then decide on the winner. Backers of Braverman were already being assiduously lobbied by other camps. One MP who supported the attorney general suggested they would move, “mostly to Liz” – potentially helping the foreign secretary to make some ground against Mordaunt. Braverman had put withdrawing from the European convention on human rights at the heart of her pitch, and said she would be seeking assurances from other candidates that they would do so. Speaking after she was eliminated from the race, she said: “I am absolutely blown away by the support that I got from lots of members of parliament, if not in their votes, then definitely in their hearts.” YouGov polling of Conservative members published on Wednesday suggested either Mordaunt could soundly beat Sunak in a head-to-head vote, or that Truss could win if pitted against him. But Sunak’s backers insisted he would push through. Mark Harper, the former chief whip who is backing Sunak, said the former chancellor was shaping the debate after a call for an end to “fairy tales” about the economy. “I’m very please he hasn’t [committed to tax cuts],” he said. “Some people are promising also massive increases in public spending as well. You have to say: ‘How you are going to pay for it?’” Harper said there had been no dirty tricks from Sunak’s campaign or votes lent to other candidates. He said the former Treasury minister Mel Stride was running the campaign’s whipping operation rather than Gavin Williamson, the former education secretary, who has earned a reputation for “dark arts” in leadership campaigns.