The Italian Prime Minister said he would have to resign if caught lying about aspiring model Noemi Letizia.
The 72-year-old conservative leader's relationship with an 18-year-old has become an explosive political issue in Italy after his wife Veronica demanded a divorce because of his womanising and said he was "not well".
Berlusconi has denied any wrongdoing or lying in his apparently contradictory explanations of why he went to Noemi Letizia's 18th birthday and gave her an expensive necklace. He has promised to explain it all in parliament but not set a date.
He told reporters in Rome that if someone asked whether he had "a relationship, let's say steamy or more than steamy, with an underage girl", his answer would be: "Absolutely not."
"I have sworn it on the life of my children. And I said that I am aware that, if this were perjury, I would have to resign a minute later," said Berlusconi, who was elected for a third time last year and enjoys strong support in opinion polls.
The flamboyant media magnate normally has the support of the Roman Catholic establishment in Italy, but it has criticised him for setting a bad example to the country's young people with his behaviour and his very public second divorce.
The age of consent for sex in Italy is 16 but people under 18 are considered minors. Letizia turned 18 last month and was photographed with Berlusconi at her birthday party, and at other social events last year when she was 17.
The opposition has targeted Berlusconi's behaviour ahead of European elections in June and centre-left leader Dario Franceschini, on the campaign trail, asked bambini-loving Italians: "Would you have your children raised by this man?"
The comment proved too much for Berlusconi's offspring. They rarely make public statements - they refused to take sides when Veronica asked for a divorce this month - but they reacted with fury to Franceschini's remark.
"Angry? I am indignant. Furious. No, this is enough," Marina, Berlusconi's daughter from his first marriage and chairman of publisher Mondadori, which is part of Berlusconi's business empire, told Corriere della Sera newspaper.
"This time, I don't intend to stay silent ... My father has always worked a lot, but there has never been a time, a single time, in which I did not have him near when I needed him."
Son Pier Silvio, deputy chairman of the Berlusconi family broadcasting company Mediaset, demanded to know in a statement how the opposition leader dared make such a "bad taste" comment and said he shared his father's values.
Berlusconi's three children with Veronica Lario also put out a statement saying they were "brought up in a family atmosphere that was balanced and full of values".
"Not everything can be put to an opinion poll. As for the question on whether a father is capable of raising a child, the only ones who can respond to that are the children themselves," Barbara, Eleonora and Luigi Berlusconi said in the statement.
"Politics should not turn to judging the role of a father, which has nothing to do with politics."