Penny Mordaunt has said other Conservative leadership campaigns are running “black ops” briefings trying to damage her because they do not want their candidate to face her in the final round of voting, by Tory party members. There has been a recent spate of negative coverage of the bookmakers’ favourite to succeed Boris Johnson, including an attack from the former Brexit negotiator David Frost, and a lengthy “dossier” in the Daily Mail, setting out Mordaunt’s supposedly liberal views. In an interview with Sky News, the trade minister said she believed she was being targeted to stop her reaching the final round of voting, in which Tory members decide between two candidates chosen by the party’s MPs. “People obviously are trying to stop me getting into the final because they don’t want to run against me,” Mordaunt said. Mordaunt remains second behind Rishi Sunak, the former chancellor, in MPs’ votes, but polling suggests she would beat any other candidate among members if she makes the final part of the race. Frost has stepped up his attacks on her, saying she was “absent on parade” when he worked with her on post-Brexit negotiations last year. Friday’s Mail featured a long article detailing what it called “troubling” facts about Mordaunt, including that she has liberal views on transgender issues, has never married, and that she and her former partner “had eight cats, but no children”. “People are going to try and stop me, and it’s right. That is right. Anyone going for this job needs to be tested and scrutinised,” Mordaunt told Sky. “You’ll see from my campaign that I’m not engaging in any of that. “I am running a positive campaign, and I’m talking in this campaign about the issues that the public are worried about … And that’s why I’m not engaging in any of these black ops.” Earlier on Friday, Frost urged Kemi Badenoch to pull out of the Tory leadership contest to bolster Liz Truss’s position in the race. Truss was picking up support from the Tory right after the attorney general, Suella Braverman, was eliminated from an increasingly bitter leadership race in which Sunak came out top and Mordaunt second in the latest round of MPs’ votes. The contest is descending into acrimony as the candidates prepare for the first TV debate on Channel 4 on Friday evening. Writing in the Daily Telegraph, Frost said: “Kemi and Suella Braverman set out convincing programmes, with differing emphases, for change. “But Liz’s depth of experience, her energy and ideas – as well as the simple fact she has the most votes of the three – put her in the lead. “It is now time for pragmatism. I urge Kemi to stand down in return for a serious job in a Truss administration.” Badenoch’s campaign, however, said she was “in it to win”. The former Conservative leader Iain Duncan Smith, who is also backing Truss, declined on Friday to directly criticise Mordaunt but emphasised Truss’s experience. He told LBC: “We can’t just elect somebody because, for a short period of time, they may look better than others. What we’re actually electing is not, in a way, a popularity contest. We’re electing somebody who has to govern for probably two years with a huge set of crises.” Braverman was knocked out of the race after receiving 27 votes in the second round. She immediately assailed Mordaunt over the issue of trans rights and later announced she would be backing Truss’s bid. Since launching her campaign Mordaunt has sought to play down the idea that she is too “woke” for the tastes of Tory members. The issue of trans rights is likely to be raised in tonight’s 90-minute debate at BT studios, which will be moderated by the Channel 4 news anchor Krishnan Guru-Murthy. The candidates will be questioned by a London audience of 50 to 100 people, most of them floating voters, with Guru-Murthy asking follow-up questions. The candidates will take turns to respond, followed by eight to 10 minutes of debate between them. They will have 45 seconds each for closing statements at the end.