Speaking at the Democratic party fund-raising lunch in Orlando, Florida, Mr Clinton said the days since the Lewinsky saga began had been the toughest of his life.
Speaking to reporters at a luncheon in the Marriott Hotel in support of Buddy MacKay, the Democratic candidate for governor of Florida in next month's elections, Mr Clinton said: "I've done my best to be your friend but I also let you down. I let my family down. I let my wife down. I let the country down. I'm determined never to let anything like that happen again." His audience of several hundred erupted into cheers and whoops.
"I'm determined to redeem the trust of the American people," the President went on to say. Referring to a visit he had made to a primary school in Orlando earlier in the day, Mr Clinton said he had shaken hands with a small boy "who reminded me very much of myself when I was that young; he said, `Mr President, I want to grow up to be president, I want to be a president like you'."
The President's voice cracking with emotion, he added: "I thought to myself I want to be able to conduct my life and my presidency so that all the parents of this country feel good ... I'll never forget that little boy at all.
"So I'm asking you for your understanding, for your forgiveness. I hope this will be a time of reconciliation and healing. I hope millions of families all over America grow stronger because of this.
"There are a whole lot of people, especially in Washington, who would like this to be the subject of the elections in November. I want your understanding. These have been the toughest days of my life. I have no one to blame but myself.
"I'm determined to redeem the trust of all the American people."
Before and after Mr Clinton's address, about 200 protesters lined a street opposite the hotel where he was speaking, carrying anti-Clinton placards and chanting: "The law will prevail."
Eileen Byrne, an Orlando radio talk-show host, had urged residents of the city to show up and protest over what she called Mr Clinton's failure to apologise outright for his conduct.
"I am a Democrat," she said. "I stood up for him all the time until he made his 17 August speech and told us otherwise. I just don't think it's right. He said `I'm sorry' in Ireland. I want to hear the words `I'm sorry' on American soil."
Around her, a crowd held placards with such slogans as "Resign you swine", "No more stains, say I'm sorry", and "Impeach Clinton".
Among the crowd was Gene McDonald, a 50-year-old businessman from Boca Raton, holding a sign saying "The Clinton Haters' Club". He said he had shown up because he had been beaten up by Clinton supporters in his home town for holding a one-man street protest last month.