Vitter, holding hands with his wife, Wendy, entered a news conference on Monday in suburban New Orleans where he again apologized for his past behavior and denied having relationships with New Orleans prostitutes.
"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 said that he and his wife had dealt with his past problems years ago and that she forgave him, reported CBS News affiliate WWL. He said that if his opponents wished to use his past failings to attack statements that he has made, "so be it."
"No matter how long ago it was, I know this hurt the relationship of trust I have enjoyed with so many of you, and I have a lot of work to do to rebuild that," he said.
He also offered no indication that he would resign. Instead, Vitter said he planned to continue working on the state's recovery after Hurricane Katrina.
"For my part, I'll be helping finalize a crucial water resources bill to provide much better hurricane and flood protection. I'll be fighting to complete I-49, Louisiana 28 and Louisiana 1 and much more," he said, adding that he planned to work for "good border and workplace security" as well.
On July 9, Vitter apologized for committing a "very serious sin in my past," acknowledging that his Washington phone number was among those called several years ago by an escort service run by Deborah Jeane Palfrey.
Federal prosecutors accuse Palfrey of racketeering by running a prostitution ring that netted more than $2 million over 13 years, beginning in 1993. She contends her escort service, Pamela Martin and Associates, was a legitimate business. Telephone records show that the service called Vitter's number five times from 1999 to 2001, while he was a U.S. representative.
Also last week, Jeanette Maier, the former madam of a New Orleans brothel that was shut down several years ago claimed Vitter was a client in the 1990s. However, her defense lawyer and a U.S. attorney who prosecuted her said Vitter's name never came up in that investigation.
The Times-Picayune newspaper in New Orleans also reported that Vitter had used the services of another New Orleans prostitute.
Vitter, 46, referred vaguely to the New Orleans-based reports but said that "those stories are not true."
At a coffee shop near where the news conference was held, Anthony Martina, 55, said he didn't vote for Vitter in the last election but probably would in the next.
After the 2005 hurricanes, Martina said he was having trouble negotiating the bureaucracy of the Federal Emergency Management Agency but Vitter and his office helped him get the recovery aid he was due.
"The man's doing his job and the people who work for him are doing their job," Martina said. "He's a man," he continued. "It (the situation) doesn't change the politics of what he's doing for the state. ... He's a human being just like anybody else. That's a family issue that I think he and his wife have to deal with. If it was a political issue, then the people would have to deal with him."
The first-term Republican said he has worked hard on his marriage and on living by the values he has long espoused as a politician.
"I believe I received forgiveness from God. I know I did from Wendy," Vitter said. "Since then, I've gotten up every morning, committed to trying to live up to the important values we believe in. If continuing to believe in and acknowledge those values causes some to attack me because of my past failings, well, so be it.
"Unfortunately, my admission has incurred some longtime political enemies and those hoping to profit from this situation to spread falsehoods, too."
Vitter did not take questions, but Wendy Vitter stepped to the podium and called her husband "my best friend."
"When David and I dealt with this years ago, I forgave David and made the decision to love him and recommit to our marriage," she said. "To forgive is not always the easy choice, but it was and is the right choice for me."
Vitter, a Harvard University graduate and Rhodes Scholar, was elected to Congress in 1999 to fill the vacancy left when Rep. Robert Livingston, R-La., resigned amid disclosures of marital indiscretions. Vitter was elected to the Senate in 2004.
U.S. Sen. Mary Landrieu, D-La., said she would have no comment on the matter until she speaks with Vitter.