Rielle Hunter's lawyer, Robert Gordon, says his client is a private individual who wishes to maintain the privacy of herself and her daughter.
In a statement, Gordon says that Hunter is ruling out any kind of testing that could establish who the daughter's father is.
"Rielle will not participate in DNA testing or any other invasion of her or her daughter's privacy now or in the future," he said.
On Friday, Edwardswith Hunter in 2006 but denied that he was the father of Hunter's 5-month-old daughter. Edwards said he will take a paternity test to prove he is not the father.
The decision by Hunter means that the issue of who the father will remain an open question.
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.
Edwards, a 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 Hunter, then 42. In an interview which aired on ABC's "Nightline" on Friday night, Edwards said he would be willing to take a paternity test to put the issue to rest but wasn't sure whether Hunter would be willing to.
"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 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."
Edwards' admission has stirred up more questions, reports CBS News correspondent Kelly Cobiella - When exactly did Edwards end the affair? And how did Hunter end up in a $3 million California home?
Fred Baron, a longtime financial backer of Edwards' campaigns, said in a statement Saturday that he helped pay for Hunter's move from North Carolina because of "harassment by supermarket tabloids," reports Cobiella.
Edwards insists he knew nothing of Baron helping Hunter move.
He also denies any knowledge of recent tabloid pictures that claim to show him holding Hunter's baby.
"I don't know anything about that photograph," Edwards said in the ABC interview. "I don't know who that baby is. I don't know if the picture has been altered, manufactured, if it's a picture of me taken some other time holding another baby. I have no idea."
In her statement Friday, Elizabeth Edwards said it wasn't easy to find out about the extramarital affair in 2006 but indicated she did not believe that her husband was the father of Hunter's daughter.
"This was our private matter, and I frankly wanted it to be private because as painful as it was I did not want to have to play it out on a public stage as well," she said. "Because of a recent string of hurtful and absurd lies in a tabloid publication, because of a picture falsely suggesting that John was spending time with a child it wrongly alleged he had fathered outside our marriage, our private matter could no longer be wholly private."
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. He recently endorsedand had been mentioned as a possible running mate. But as rumors spread of Edwards' possible affair it became clear that he would not likely speak at the Democratic National Convention later this month in Denver.