Lord Frost said she lacked a grasp of the detail, was unwilling to deliver tough messages to Brussels, and that he had to ask Boris Johnson to replace her.
He said he has “grave reservations” about whether Ms Mordaunt – who is currently the international trade minister – is now fit to be the next prime minister.
He told TalkTV: “I would not feel able to serve in a ministerial team under Penny Mordaunt. That’s how strongly I feel about that. I felt I had to make that clear today. MPs are voting today and I think they need to know the facts.
Ex Cabinet minister Lord Frost has "grave reservations" about Penny Mordaunt becoming the next PM.
"I am surprised at where she is in this leadership race. She was my deputy. She wasn't fully accountable or visible. I had to ask the PM to move her on"@JuliaHB1 | @DavidGHFrost pic.twitter.com/fju9f5QguN
— TalkTV (@TalkTV) July 14, 2022
“The party has made wrong choices in recent years and I want to make sure we make the right one this time, so I had to make my views clear.”
His onslaught came after Ms Mordaunt took second place in the first round of voting by MPs, putting her in a prime position to make it through to the final ballot of party members.
Lord Frost continued: “I am quite surprised at where she is in this leadership race. She was my deputy – notionally, more than really – in the Brexit talks last year.
“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 fully accountable, she wasn’t always visible. Sometimes I didn’t even know where she was. This became such a problem that, after six months, I had to ask the Prime Minister to move her on and find somebody else to support me.”
He added: “If you are a prime minister you have got to be able to take responsibility, you have got to be able to run the machine, you have got to be able to take tough decisions, deliver tough messages.
“Anybody can be photo’d in a video with I Vow To Thee My Country, but it is what you do in practice. Are you able to be tough, are you able to lead, are you able to take responsibility?
“From the basis of what I saw, I’m afraid I would have grave reservations about that.”
— Simon Clarke MP (@SimonClarkeMP) July 14, 2022
Asked whether Brexit would be safe in Ms Mordaunt’s hands, Lord Frost said: “I would worry, on the basis of what I have seen, we wouldn’t necessarily get that from Penny.”
A social media link to a clip of his interview was retweeted by Treasury Chief Secretary Simon Clarke – who is backing Liz Truss for leader.
Mr Clarke said: “Lord Frost’s warning is a really serious one. Conservatives – and, far more importantly, our country – need a leader who is tested and ready.”
Lord Frost said he had not yet decided who to support in the leadership race but that Ms Truss, Kemi Badenoch and Suella Braverman are all saying “very interesting things, things that the country needs to hear”.