The British foreign secretary is bidding to consolidate and increase support from the right of the Conservative Party in the leadership contest, in the face of a surge by the trade minister.
Rishi Sunak, the former British chancellor, came out on top of Thursday’s voting, and in second was Ms Mordaunt, who was bearing the brunt of the attacks from rival camps as she gained the most momentum.
Britain’s transport minister and Truss backer Wendy Morton, appearing on Times Radio, said she is “absolutely not” involved in any kind of untoward campaign.
Former cabinet minister David Davis, a supporter of Ms Mordaunt, had called out “black ops” being directed at her.
Ms Morton said: “What I am involved in is a campaign to get Liz Truss elected as the next leader of the Conservative Party because I happen to think, I know, that she’s the right candidate.
“I worked with her at the Foreign Office and I saw first hand how hard-working she is, how dedicated she is, and how she just gets on with the job and she delivers.”
She said the Truss camp is not concerned about the lead Ms Mordaunt has maintained in the first two ballots, indicating hopes that Tory MPs might get behind her candidate.
Ms Morton added: “You know, we have still got rounds of voting to go, there are still candidates, there are colleagues out there who have not declared for a candidate, there are colleagues who have voted for candidates who have now dropped out of the race. So it’s all to play for.”
Suella Braverman, Britain’s Attorney General, came out in support of Ms Truss after being eliminated from the contest.
She fared the worst in the second round of voting and was eliminated to leave five contenders who will take part in the first televised debate on Friday evening.
Ms Braverman described Ms Truss as the “best person to unleash the opportunities of Brexit” and deliver tax cuts, as the right of the party seeks to rally round a single candidate.
Taking influential Tory Steve Baker’s vote with her, it was a blow to Kemi Badenoch, who was facing pressure to pull out and back Ms Truss to keep Mr Sunak or Ms Mordaunt out of No 10.
Sources close to Ms Braverman told the PA news agency she made the decision after holding talks with Ms Truss.
In a statement, Ms Braverman said: “I’m confident she (Ms Truss) will defend free speech, champion equality of opportunity and take a robust line on illegal immigration.”
Ms Mordaunt has faced a scathing attack from former Britain’s Brexit minister Lord Frost, who also urged Ms Badenoch to pull out of the Tory leadership contest so there can be “unity among free marketeers”.
Lord Frost, seen as an influential figure about the Tory Party grassroots, described Ms Mordaunt as “absent on parade” when he worked with her on post-Brexit negotiations last year.
Tory MP Dame Maria Miller, pressed on whether Ms Mordaunt could fall victim to dirty tactics as she seeks to replace Mr Johnson, said her candidate wanted a positive campaign.
“Penny’s support among Members of Parliament has grown, and that is the same throughout the country,” Dame Maria told Sky News.
She said polling is showing that her “support base is growing”.
Dame Maria added: “This leadership contest is run along a set of lines and I think people will want it to be a positive campaign. We’re colleagues, together, we’re not opposing each other in a fundamental political sense.
“It is just about getting a new leader.”
Dame Maria, a Mordaunt backer, shrugged off the criticism from Lord Frost.
She told Sky News on Friday: “I have seen her to be a very effective campaigner. She really is one of the leading proponents of Brexit and was throughout the campaign.”
Mr Sunak picked up 101 votes in the second ballot, Ms Mordaunt 83, Ms Truss 64, Ms Badenoch 49 and Tom Tugendhat 32.
Mr Tugendhat, despite dropping five votes, insisted he would not quit the race as the remaining contenders progress to a round of televised debates.
“I have never turned down a challenge because the odds were against me. I don’t plan to start now,” the senior backbencher said.
His allies are hoping that his fortunes can be reversed by a strong performance in the TV debates over the coming days, with backer Tory MP Jake Berry stressing that it will be a “key weekend” for his candidate.
Ms Badenoch’s campaign, however, has also said she is “in it to win”.
Channel 4 said all five candidates have confirmed they will take part in its debate on Friday night, with further televised clashes scheduled for Sunday and Tuesday.
The next round of voting is due on Monday, with subsequent rounds if required until two candidates are left, who will then battle it out over the summer to win the support of Conservative members.
Their choice of the next prime minister will be announced on September 5th.
Mr Johnson will then formally tender his resignation to Britain’s Queen Elizabeth II to make way for his successor the following day.