London mayor Boris Johnson says BBC presenter Eddie Mair did a "splendid job" in questioning him about his "integrity" during an interview.
Mr Johnson was asked whether he was a "nasty bit of work", causing his father to complain of "disgusting" journalism.
But Mr Johnson said Mr Mair had been "perfectly within his rights to have a bash at me" on the Andrew Marr Show
Prime Minister David Cameron said the mayor's "ability to get out of a spot" should not be underestimated.
Mr Johnson is often vaunted as a possible successor to the Conservative leader, although he is not currently a Member of Parliament.
During the interview, on Sunday, he was questioned over suggestions he had lied about having an extra-marital affair and had made up a quotation, for which he had been dismissed, while working as a journalist on the Times newspaper.
This exasperated the mayor's father, Stanley Johnson, who told the radio station LBC: "Eddie Mair's interview was about the most disgusting piece of journalism I've listened to for a very long time.
"The BBC sank about as low as it could. If grilling people about their private lives, accusing them of guilt by association and openly abusing them is a legitimate interview, then frankly, I don't know where we are coming."
But, appearing at an event in London, the mayor seemed less upset, saying: "Eddie Mair did a splendid job. There is no doubt that is what the BBC is for - holding us to account.
"I fully concede it wasn't my most blistering performance, but that was basically because I was set to talk about the Olympics and housing in London and he wanted to talk about other things, some of them - my private life and so on - of quite some antiquity, the details of which I wasn't brilliant on.
"He was perfectly within his rights to have a bash at me - in fact it would have been shocking if he hadn't. If a BBC presenter can't attack a nasty Tory politician, what's the world coming to?"
Asked whether Mr Mair should get Jeremy Paxman's presenting role on BBC Two's Newsnight programme, he added: "I should think he'll get an Oscar. It was an Oscar-winning performance. I think he'll get a Pulitzer [Prize]."
During the Andrew Marr Show, Mr Johnson was pressed over whether he had lied to Conservative leader Michael Howard about allegations of an affair in 2004 - which resulted in his resignation as shadow arts minister - as well as claims he had been sacked from the Times during the late 1980s.
Insisting that he was talking about "integrity", Mr Mair turned to a 1990 telephone conversation Mr Johnson had had with one of his friends, Darius Guppy, who had been demanding the private address of a News of the World journalist.
A recording of the call suggested Mr Johnson had agreed to supply the details, even though Guppy, who was later jailed for fraud, had indicated he had wanted to have the reporter, who had been investigating his affairs, beaten up.
Mr Johnson stressed that "nothing eventuated" from the conversation, adding: "If any of us had our phone conversations bugged people say all sorts of fantastical things whilst talking to their friends."
Mr Mair asked: "You are a nasty bit of work, aren't you?"
Mr Johnson replied: "All three things I would dispute... if we had a longer time I could explain that I think all three interpretations you are putting on these things are not wholly fair."
Questioned about the interview during a visit to Ipswich, Mr Cameron said: "Never attempt to limit Boris's ability to get out of a spot. He's doing a fabulous job as mayor of London."
The interview came ahead of a documentary on the mayor's life and career, Boris Johnson: The Irresistible Rise, which will be broadcast on BBC Two from 21:00 GMT on Monday.