CNN's Carol Costello reports Sen. Vitter faces new prostitute allegations.

WASHINGTON (CNN) - Republican Sen. David Vitter, who admitted earlier this year to a "very serious sin" after his telephone number appeared in the telephone records of a Washington, DC escort service, faced new allegations Tuesday he had a relationship with a prostitute from his home state of Louisiana.

With Hustler magazine publisher Larry Flynt at her side, the former prostitute Wendy Ellis told reporters that Vitter employed her services several times a week between July and November of 1999. At the time, Vitter was a new face Capitol Hill, having won a special election only months earlier.

"I want the truth to be known," Ellis said. "It was a pure sexual relationship. He would come in and do his business."

Vitter, who acknowledged in July to contacting an escort service after Hustler reported his number was linked to the alleged 'DC Madam' Deborah Jeanne Palfrey,' has denied any links to Louisiana prostitutes.

"My admission has encouraged long-time political enemies and those hoping to profit from the situation to spread falsehoods, like those New Orleans stories in recent reporting,” Vitter said in July. “Those stories are not true.”

On Tuesday, Flynt said Ellis' passed a polygraph test, but he had no other evidence linking the senator to the former prostitute.

"We don't even like to mix polygraphs into this stuff, because they're not admissible in court," he said. "But you know she's concerned that she be believed as much as Vitter is believed."

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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.

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Larry Flynt said Wednesday he doesn’t want Vitter, above, “legislating for me.”

WASHINGTON (CNN) - Hustler publisher Larry Flynt took credit Wednesday for exposing Sen. David Vitter as a client of a D.C. prostitute, saying he did so to uncover the Louisiana Republican’s hypocrisy.

“I very seldom get a chance to get a big one, and sometimes I have to go bottom feeding,” Flynt said at a late afternoon news conference. “We have a criteria, and that is if someone is living a life contrary to the way they are advocating - their personal life - than they become fair game.”

Vitter admitted Monday that his telephone number turned up in the phone records of an escort service run by Deborah Jeane Palfrey, though he did not say he had sex with a prostitute. The records date from before he won his Senate seat in 2004.

On Tuesday, Hustler magazine claimed credit for exposing Vitter's connection to the "D.C. Madam,” saying he confessed after a journalist reported finding the senator's number in the escort service's phone records.

In Wednesday’s press conference, Flynt said, “I don’t want a man like that legislating for me, especially in the areas of morality.”

Vitter heavily campaigned on social values in his 2004 Senate race and was one of the top backers of a failed constitutional amendment that would have banned same-sex marriage.

The Louisiana Republican issued a statement Monday night calling his contact with Palfrey a “very serious sin,” but has since not been seen in public.

- CNN Ticker Producer Alexander Mooney