But in the same speech, he cited the value of "truthfulness" and how it's the first pillar of good character.
Reached at his home in Washington on Wednesday, Domenici said he had nothing more to say. Domenici and his wife have been married more than 50 years and have eight children.
The scandal has all the elements of an inside-the-Beltway soap opera.
Michelle Laxalt is the daughter of former U.S. Sen. Paul Laxalt, himself a significant political figure in the 1970s and '80s as he served as Nevada governor and two terms in the Senate alongside Domenici.
Michelle Laxalt became a prominent lobbyist, Republican activist and television commentator after the affair. She said in the statement that she chose to raise her son as a single parent and that the two agreed that it would be a private matter.
"One night's mistake led to pregnancy more than 30 years ago," she said.
Laxalt's prominence in national politics occasionally put her in an odd position of publicly discussing the integrity of the man who is the father of her child.
In 2008, Domenici was reprimanded by the Senate ethics committee for his involvement in a scandal over the Bush administration's firing of eight U.S. attorneys.
At the time, Laxalt defended Domenici's integrity on CNN, calling him an honorable man who was supporting "no fewer than eight children."