NEW ORLEANS — A former New Orleans prostitute who says she had an affair with Sen. David Vitter has passed a lie-detector test and will provide details of the four-month relationship at a press conference Tuesday, according to Hustler magazine publisher Larry Flynt.

Wendy Cortez, whose real name is Wendy Ellis, says she had a sexual relationship with Vitter, R-La., in 1999, when he was a state legislator.

Copies of the results of Cortez’s polygraph test, which she took at Flynt’s request, will be provided to reporters at the news conference at Flynt’s office in Beverly Hills, Calif., Hustler said in a news release Monday.

Vitter spokesman Joel Digrado wouldn’t comment on the Flynt news conference. In an e-mail, Digrado said, “Sen. Vitter and his wife have addressed all of this very directly. The senator is focused on important Louisiana priorities like the water resources bill and the Iraq debate.”

Vitter, 46, apologized in July for committing a “very serious sin” and acknowledged his Washington phone number was among those called several years ago by an escort service run by Deborah Jeane Palfrey. The admission came after Flynt’s Hustler magazine told the senator that his telephone number was linked to Palfrey’s escort service.

Flynt has offered to pay $1 million to anyone who can show he or she had a sexual encounter with a member of Congress or a high-ranking government official. It is unclear whether he has offered Cortez any money.

Vitter, a first-term senator elected in 2004, has denied having relationships with New Orleans prostitutes. In a call-in radio show during the Senate campaign, he dismissed as “absolutely and completely untrue” that he had a relationship with a Wendy Cortez.