McClatchy Newspapers had reported that Domenici and Rep. Heather Wilson, R-N.M., pressured former U.S. Attorney for New Mexico David C. Iglesias to expedite indictments of a Democratic politician prior to the 2006 election.
Wilson was involved at the time in a hotly contested re-election campaign, which she won by 875 votes out of more than 210,000 cast.
At first Domenici said he didn't know what Iglesias was talking about. Sunday, he issued a statement admitting he called Iglesias, but denying he pressured the former prosecutor.
"In retrospect, I regret making that call and I apologize," Domenici said.
He said he had told Justice Department officials that Iglesias should be replaced, but he said that occurred before he called Iglesias about the corruption investigation, the Washington Post reported.
Iglesias, who resigned Wednesday as U.S. Attorney for New Mexico, told the Post he suspected complaints from lawmakers, whom he has not named, may have led to his firing.