NEW ORLEANS -- With his wife, Wendy, at his side, Louisiana U.S. Sen. David Vitter said Monday he will not resign, a week after he admitted to a connection with the so-called D.C. Madam.

Vitter made the comments during a news conference in Metairie, La., his hometown, after a week in seclusion. He said he wanted time alone with his family and for prayer.

"I want to again offer my deep, sincere apologies to all those I have let down and disappointed with actions from my past," Vitter said. "I am completely responsible and I am so very, very sorry."

Vitter, who is Catholic, said he confessed about his indiscretions a number of years ago.

"I believe I received forgiveness from God. I know I did from Wendy," he said. "Unfortunately my admission has incurred some longtime political enemies and those hoping to profit from this situation."

Vitter is a conservative who ran for office on a platform opposing abortion and supporting a constitutional amendment banning gay marriage. Before being elected to the Senate, he replaced former Louisiana Democratic Rep. Bob Livingston, who resigned after rumors of numerous affairs. Vitter was critical of Livingston's behavior, and at the time said that former President Bill Clinton should have also resigned when his affair with Monica Lewinsky was made public.

"I think Livingston’s stepping down makes a very powerful argument that Clinton should resign as well and move beyond this mess,” Vitter said in a December 1998 commentary in the Atlanta Journal-Constitution.

Hustler magazine publisher Larry Flynt played a role in exposing both men's activities.

Flynt said last week that his magazine was the first to link Vitter to an escort service operated by Deborah Jeane Palfrey. She is accused of running an escort service in Washington, D.C., a charge she denies.

Vitter acknowledged last Monday that his telephone number appeared among others in Palfrey's records.

He made the admission to The Associated Press in a statement. Flynt said Vitter went to the AP only after one of his reporters contacted Vitter to confirm the connection to Palfrey.

Flynt said Vitter was fair game in a sex scandal investigation because he advocated conservative positions while living a private life at odds with his public life.

"Sometimes I have to go bottom feeding" in an effort to remove "phonies" from lawmaking positions, Flynt said in a news conference at his magazine's offices.

He said his staff called Vitter's office Monday, saying they knew his telephone number appeared on a list from Palfrey's escort service. Vitter then went to The Associated Press in an attempt to get ahead of the story, Flynt said.