Cherie Blair, the prime minister's wife, has denied claims that her husband considered standing down earlier this year.
Mrs Blair gave her first television interview to Channel 4
Mrs Blair said she would have been "one of the first people to know" if the allegations were true.
Lord Melvyn Bragg made the claims, saying the prime minister had been under a "colossal strain".
Mrs Blair told Woman's Hour on BBC Radio 4, that Lord Bragg, a family friend, was "mortified" by his remark.
Mr Bragg said Mr Blair's strain was "personal and family" stress, creating a media frenzy.
Appearing on Channel 4's Richard and Judy show, Mrs Blair denied
that the Labour peer had been briefed to make the comments.
Taking part in her first ever television interview, she said: "As Tony himself said, there never was a moment when he was going to resign. I can assure you if he had done, I would have known.
"So I do not know where Melvyn got it from and to be honest I think he is
mortified that he said it."
She went on to deny that the remarks had broken their friendship.
Asked why she thought Lord Bragg had made the comments, Mrs Blair replied: "I don't know, you'll have to ask him."
'Ill advised' comments
"We can't always explain what goes on in men's minds - I wish I could."
Lord Bragg's wife, Cate Haste, who was also interviewed on Radio 4, echoed these sentiments, saying she did not think her husband knew what he was talking about.
She went on to say his comments had been ill advised and that he should stick to arts programmes.
Mrs Blair conducted the interviews while promoting her book The Goldfish Bowl, which looks at the life of a spouse in Downing Street.
The book was co-written by Lord Bragg's wife.