WASHINGTON (CNN) -- There are no indications Sen. David Vitter will leave the Senate early after being linked to an alleged prostitution service, said a Capitol Hill colleague and close friend on Friday.
Sen. David Vitter apologized after his telephone number appeared among those linked to an escort service.
Sen. Jim DeMint of South Carolina has been exchanging e-mail with Vitter, a fellow Republican from Louisiana who's been missing from the Senate since the allegations surfaced Monday.
Vitter plans to return to work in time for lawmakers' first scheduled vote next Tuesday, DeMint said.
"It's my hope he can work through this -- keep a low profile for a while," said DeMint, who added that he hadn't discussed details of the allegations with Vitter.
The records were dated before 2004, when Vitter was first elected to the Senate, where Democrats enjoy a razor-thin majority in a delicate balance of power.
DeMint said Vitter's Senate colleagues are "very anxious to help him get through this," and offered some perspective on the scandal.
"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," DeMint said. "And we might want to remember some of those."
"He seems to be handling it in a very responsible way," said DeMint. "He is saying he was wrong."
In a statement distributed to reporters on Monday, Vitter acknowledged the incident as "a very serious sin in my past for which I am, of course, completely responsible. "Several years ago, I asked for and received forgiveness from God and from my wife in confession and marriage counseling."
"I can't say what he's going to do," DeMint said. "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."
Vitter is married with four children ages 13 and under, according to his Web site.
"Obviously, he has a whole lot of remorse and wants to put this behind him," DeMint told CNN. "This is something he'd gotten out with his wife and family long before. Just none of the rest of us knew about it."
DeMint said he didn't know whether Vitter plans to address the matter again publicly any time soon.
Government prosecutors say Pamela Martin and Associates was a prostitution ring that Palfrey operated in the Washington area for 13 years. Palfrey denies that her business provided sexual services to its customers. E-mail to a friend