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, Edwards admitted to having an extramarital affair with 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."
