Vitter is expected to return to the Senate next week.
WASHINGTON (CNN) - Embattled Sen. David Vitter, R-Louisiana - who has not been seen on Capitol Hill since allegations were raised Monday he used a D.C. prostitution service - will return to the Senate next week, just in time for the first scheduled vote of the week on Tuesday, according to Sen. Jim DeMint, R-South Carolina., who has exchanged e-mails with Vitter.
"Obviously, he has a whole lot of remorse and wants to put this behind him. He seems to be handling it in a very responsible way. He is saying he was wrong. He made terrible mistakes. He is not trying to diminish the problem," said DeMint who is the first person CNN has spoken to who has communicated directly with Vitter since the scandal broke.
Vitter admitted Monday that his telephone number turned up in the phone records of an escort service run by Deborah Jeane Palfrey, the woman dubbed the “D.C. Madam." The records date from before he won his Senate seat in 2004.
"This was a very serious sin in my past for which I am, of course, completely responsible," Vitter said in a statement given to reporters Monday night. "Several years ago, I asked for and received forgiveness from God and from my wife in confession and marriage counseling."
DeMint said there are no indications that Vitter, a first-term senator who is married with children, will leave the Senate.
"He'll be back next week," said DeMint who is close with Vitter.
DeMint said he doesn't know whether or Vitter plans a news conference or any other public statement that would go beyond a short written statement he issued earlier this week in which he acknowledged, "a very serious sin in my past."
"I can't say what he's going to do. But he seems to want to address it head on and not want to hide from the mistakes that he's made. He's not trying to cover it up. This is something he'd gotten out with his wife and family long before just none of the rest of us knew about it. I look forward to him just trying to do everything he can so he can go on," DeMint said.
DeMint said he has not discussed the details of the allegations against Vitter. When he returns, Vitter won't be the only senator who has a "moral disaster" in his past," DeMint said.
"From what I've heard from other senators is they're very anxious to help him get through this and again no one is trying to diminish that this is a huge moral failing that reflects poorly on the whole body whenever that happens. For that, I know he's sorry.
"But it's my hope he can work through this. Keep a low profile for a while. But there are many senators out there on the Senate floor who have had moral disasters in their past that have weathered it and been here for decades. And we might want to remember some of those," he said.
– CNN Congressional Producer Ted Barrett