WASHINGTON >> A Justice Department investigation into Rep. Matt Gaetz and an indicted Florida politician is focusing on their involvement with multiple women who were recruited online for sex and received cash payments, according to people close to the investigation and text messages and payment receipts reviewed by The New York Times.

Investigators believe Joel Greenberg, the former tax collector in Seminole County, Florida, who was indicted last year on a federal sex trafficking charge and other crimes, initially met the women through websites that connect people who go on dates in exchange for gifts, fine dining, travel and allowances, according to three people with knowledge of the encounters. Greenberg introduced the women to Gaetz, who also had sex with them, the people said.

One of the women who had sex with both men also agreed to have sex with an unidentified associate of theirs in Florida Republican politics, according to a person familiar with the arrangement. Greenberg had initially contacted her online and introduced her to Gaetz, the person said.

Gaetz denied ever paying a woman for sex.

The Justice Department inquiry is also examining whether Gaetz had sex with a 17-year-old girl and whether she received anything of material value, according to four people familiar with the investigation. The sex trafficking count against Greenberg involved the same girl, according to two people briefed on the investigation.

The authorities have also investigated whether other men connected to Gaetz and Greenberg had sex with the 17-year-old, two of the people said.

Gaetz, 38, was elected to Congress in 2016 and became one of former President Donald Trump’s most outspoken advocates.

The Times has reviewed receipts from Cash App, a mobile payments app, and Apple Pay that show payments from Gaetz and Greenberg to one of the women, and a payment from Greenberg to a second woman. The women told their friends that the payments were for sex with the two men, according to two people familiar with the conversations.

In encounters during 2019 and 2020, Gaetz and Greenberg instructed the women to meet at certain times and places, often at hotels around Florida, and would tell them the amount of money they were willing to pay, according to the messages and interviews.

One person said that the men also paid in cash, sometimes withdrawn from a hotel ATM.

Some of the men and women took ecstasy, an illegal hallucinogenic drug, before having sex, including Gaetz, two people familiar with the encounters said.

In some cases, Gaetz asked women to help find others who might be interested in having sex with him and his friends, according to two people familiar with those conversations. Should anyone inquire about their relationships, one person said, Gaetz told the women to say that he had paid for hotel rooms and dinners as part of their dates.

The FBI has questioned multiple women involved in the encounters, including as recently as January, to establish details of their relationships with Gaetz and his friends, according to text messages and two people familiar with the interviews.

No charges have been brought against Gaetz, and the extent of his criminal exposure is unclear. Gaetz’s office issued a statement tonight in a response to a request for comment.

“Matt Gaetz has never paid for sex,” the statement said. “Matt Gaetz refutes all the disgusting allegations completely. Matt Gaetz has never ever been on any such websites whatsoever. Matt Gaetz cherishes the relationships in his past and looks forward to marrying the love of his life.”

A lawyer for Greenberg, Fritz Scheller, declined to comment, as did a Justice Department spokesman.

It is not illegal to provide adults with free hotel stays, meals and other gifts, but if prosecutors think they can prove that the payments to the women were for sex, they could accuse Gaetz of trafficking the women under “force, fraud or coercion.” For example, prosecutors have filed trafficking charges against people suspected of providing drugs in exchange for sex because feeding another person’s drug habit could be seen as a form of coercion.

It is also a violation of federal child sex trafficking law to provide someone under 18 with anything of value in exchange for sex, which can include meals, hotels, drugs, alcohol or cigarettes. A conviction carries a 10-year mandatory minimum prison sentence.

The investigation stems from the Justice Department’s continuing inquiry into Greenberg, who potentially faces decades in prison on three dozen charges. The U.S. attorney’s office in Central Florida initially secured an indictment against Greenberg in June, alleging that he had stalked a political rival and had used his elected office to create fake identification cards.

During the investigation, the authorities discovered evidence that prompted them to broaden it, and Greenberg was indicted in August on the sex trafficking charge.

One of the sites the men met women through was called Seeking Arrangement, which describes itself as a place where wealthy people find attractive companions and pamper them “with fine dinners, exotic trips and allowances.” The site’s founder has said it has 20 million members worldwide. The FBI mentioned the website in a conversation with at least one potential witness, according to a person familiar with the conversation.

Greenberg was indicted this week on additional charges, accusing him of submitting false claims to receive pandemic relief aid from the government and trying to bribe a government official. The authorities said Greenberg undertook those efforts after he was initially indicted last summer.

Greenberg, who has pleaded not guilty to the earlier charges, is scheduled to go on trial in June. He was sent to jail in March for violating the terms of his bail.

Gaetz said this week that his lawyers had been in touch with the Justice Department and that he was the subject, not the target, of an investigation. Subjects of investigations are often witnesses or people who might have information that could help the government pursue its targets. But it is common for that designation to shift over the course of an investigation.

“I only know that it has to do with women,” Gaetz said. “I have a suspicion that someone is trying to recategorize my generosity to ex-girlfriends as something more untoward.”

Gaetz, a lawyer, was first elected to the House representing the Florida Panhandle at age 34. The son of a former president of the Florida state Senate, Gaetz attended Florida State University and William & Mary Law School before serving in the Florida Legislature.

Gaetz has sought to divert attention from the Justice Department investigation by claiming that he and his father were the targets of an extortion plot by two men trying to secure funding for a separate venture.

The men — Robert Kent, a former Air Force intelligence officer who runs a consulting business, and Stephen Alford, a real estate developer who has been convicted of fraud — approached Gaetz’s father, Don Gaetz, about funding their efforts to locate Robert A. Levinson, an American hostage held in Iran. They suggested to Don Gaetz that Levinson’s successful return could somehow be used to secure a pardon for Matt Gaetz if he were charged with federal crimes, according to a copy of their proposal provided to The Times.

Soon after, Don Gaetz hired a lawyer and contacted the FBI. Matt Gaetz said his father wore a wire and taped a meeting and a telephone conversation with Alford. An email exchange between Don Gaetz’s lawyer and the Justice Department provided to The Times appears to confirm he was generally cooperating with the FBI as it looked into his claims.

Kent denied the Gaetzes’ assertions. He said he had heard rumors that Matt Gaetz might be under investigation and mentioned them only to sweeten his proposal. “I told him I’m not trying to extort, but if this were true, he might be interested in doing something good,” Kent said in an interview.

Last year, the Trump administration notified the family of Levinson, a former FBI agent, that he had died while in captivity in Iran, where he disappeared in 2007 while on an unauthorized mission for the CIA.

But some people involved with the Levinson case continued to believe that he might still be alive, including Kent.