McGreevey said the encounters happened, but the couple needs to move forward for the sake of their 6-year-old daughter.
"This happened, this happened in the past, and now we need to move on with our lives," McGreevey said.
Dina Matos McGreevey said Pedersen's published claims are "completely false" and were prompted by the nation's first openly gay governor as a way to discredit her.
The McGreeveys are in the midst of an acrimonious divorce. She accuses him of hiding his homosexuality before and during their marriage and has sued for damages. He has said she should have known he was gay.
Pedersen said he came forward because he was angry that Matos McGreevey was offering television commentary - in which she said she was blindsided when her husband announced his homosexuality - on the resignation of New York Gov. Eliot Spitzer, who was embroiled in a sex scandal with a call girl.
McGreevey resigned in disgrace in 2004 after acknowledging an affair with a male staffer who he said was trying to blackmail him. The ex-staffer said he was sexually harassed by the Democratic governor.
The McGreeveys separated shortly after McGreevey's nationally televised speech, in which he declared himself "a gay American."
