“It is no coincidence that it was being peddled before the election,” Mr. Menendez, who has declined requests by The Times for an interview, said during an appearance in New Jersey on Feb. 9. “No coincidence that it gets peddled again as I assume the chairmanship, no coincidence that we have someone who never’s willing to meet anyone in the press or otherwise never is willing to speak to anybody on the phone, that uses a pseudonym and never shows their face.”

The background story of how the accusations were initially made has all the makings of a Hollywood political thriller, even snaring the Federal Bureau of Investigation in the process. It began in April, when an unsolicited e-mail was sent to a left-leaning group called Citizens for Responsibility and Ethics in Washington, which in a way is the liberal counterpart to Mr. Boehm’s group.

“My duty as a U.S. citizen obligates me to report what I consider to be a grave violation of the most fundamental codes of conduct that a politician of my country must follow,” said the first sentence of the e-mail, sent by a person who identified himself as Peter Williams. The e-mail, and others that followed, then went on to detail claims related to Mr. Menendez and the underage prostitutes, as well as decadent outings on a yacht.

But there was something immediately suspicious about Mr. Williams, said Melanie Sloan, a former federal prosecutor who is now executive director of Citizens for Responsibility, which is based in Washington. Mr. Williams provided some accurate details about Dr. Melgen’s life in the Dominican Republic, but would not agree to speak by phone, and he also said he had been aware of Mr. Menendez’s activities since 2008 — but was only now coming forward. That, Ms. Sloan observed, was seven months before Mr. Menendez faced re-election.

Pete Williams is the nickname of former Senator Harrison A. Williams Jr., Democrat of New Jersey; in 1983, he became the first senator jailed in 80 years, for his role in the so-called Abscam case, in which agents posing as Arab sheiks offered bribes to members of Congress. Perhaps in adopting that name, the person who sent the e-mail about Mr. Menendez was making a cruel joke.

Mr. Menendez has been a target of Republican operatives before, including during his first bid for the Senate, in 2006, when his Republican opponent, secretly at first, started work on a documentary film that was going to examine allegations of corruption early in Mr. Menendez’s career. The effort was led by a Republican opposition researcher named Chris Lyon, but the film was canceled after The Times disclosed that Mr. Menendez’s Republican opponent actually was financing the effort.