The revelation shattered the family-friendly image he had cultivated and drained the reservoir of sympathy he had built up when he campaigned side by side with his cancer-stricken wife, Elizabeth.
The political damage is so severe that Edwards, mentioned as a possible running mate to Barack Obama, is not expected to show up at the Democratic convention this month in Denver.
Edwards admitted in shame to the affair in 2006 with a videographer as he prepared to launch his White House campaign.
Acknowledging a sex scandal he had dismissed as "tabloid trash" only last month, Edwards said he had told his wife and family long ago, but "I had hoped that it would never become public."
"I am and have been willing to take any test necessary to establish the fact that I am not the father of any baby, and I am truly hopeful that a test will be done so this fact can be definitively established," Edwards said.
The former North Carolina senator, who was the Democratic vice presidential nominee in 2004, confessed to ABC News that he had lied repeatedly about the affair with Rielle Hunter, then 42.
Hunter's daughter, Frances Quinn Hunter, was born on Feb. 27 this year, and no father's name is given on the birth certificate filed in California.
A former Edwards campaign staff member professes to be the father.
In a statement provided to The Associated Press, Elizabeth Edwards confirmed that her husband had confessed the extramarital affair to her in 2006 but that after a "long and painful process" she was now standing by him.
After the story broke Friday, Edwards released a statement that said, "In 2006, I made a serious error in judgment and conducted myself in a way that was disloyal to my family and to my core beliefs. I recognized my mistake, and I told my wife that I had a liaison with another woman, and I asked for her forgiveness.
Although I was honest in every painful detail with my family, I did not tell the public."
Edwards declared his presidential candidacy in December 2006.
His wife campaigned enthusiastically with him and by herself in the months that followed. She announced in March 2007 that her cancer, formerly in remission, had returned and there apparently was no cure.
Edwards dropped out midway through this year's primaries after it became apparent he could not keep up with front-runners Obama and Hillary Rodham Clinton. He recently endorsed Obama.
Speaking to reporters Friday in Honolulu, Obama praised Edwards as a "great champion of working people" during the campaign and said the couple probably would not attend the party's convention in Denver.
"I think they need to work through that process of healing," Obama said.
Edwards was John Kerry's running mate in 2004 when Kerry lost to President Bush.
In his statement, Edwards said, "In the course of several campaigns, I started to believe that I was special and became increasingly egocentric and narcissistic. If you want to beat me up feel free. You cannot beat me up more than I have already beaten up myself."
In her statement Friday, Elizabeth Edwards said it wasn't easy to find out about the extramarital affair in 2006. She called the affair a "terrible mistake" but said the healing process was "oddly made somewhat easier" after her diagnosis of breast cancer in March 2007.
Mrs. Edwards said her family has been through a lot and pleaded for privacy.
The National Enquirer first reported on the affair in October 2007, in the run-up to the Democratic primaries, and Edwards denied it.
Last month, the Enquirer carried another story - the blaring headline referred to an Edwards "love child" - stating that its reporters had accosted Edwards in a Los Angeles hotel where he had met with Hunter after her child's birth. Edwards called it "tabloid trash."
In an interview which aired on ABC News' "Nightline" Friday night, Edwards described the affair as being "over for a long time." He declined to give specifics, saying his family was "entitled to every detail" but no one else.
Edwards acknowledged his wife was "mad, she was angry - furious would be a good way to describe it" when he told her about the affair but that he had asked her not to appear with him during Friday's interview even though she forgave him. That's because "she should not be involved in protecting me from whatever the consequences of this are," he said.
Edwards also said the tabloid was correct when it reported on his meeting with Hunter at the Beverly Hills Hilton last month and that it would be the American people's "judgment to make" as to what they think of him now after trusting him.
The Edwardses have three children - Cate, Jack and Emma Claire.
Another son, Wade, died at 16 in a 1996 car accident.
In his statement, Edwards denied making any payments to Hunter or "or to the apparent father of the baby." Late Friday, Dallas-based attorney Fred Baron, former national finance chairman for Edwards, said in a statement he decided on his own to "help two friends and former colleagues rebuild their lives when harassment by supermarket tabloids made it impossible for them to move forward on their own."
Baron didn't mention anyone by name in his statement. He said the assistance was offered and accepted without the knowledge of Edwards or anyone else.
In 2006, Edwards' political action committee paid $100,000 in a four-month span to a newly formed company run by Hunter, who directed the production of four Web videos showing Edwards in supposedly candid moments as well as in a public speech talking about morality.
The payments from Edwards' One America Committee to Midline Groove Productions LLC started on July 5, 2006, five days after Hunter incorporated the firm in Delaware.
Midline provided "Website/Internet services," according to reports that Edwards' PAC filed with the Federal Election Commission.
Edwards' PAC followed the six-figure payment with two smaller payments totaling $14,461, the last on April 1, 2007.
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