Mr. Menendez has vehemently denied the allegations. During an initial investigation, two women who had told The Daily Caller, a conservative website, in a video that Mr. Menendez had paid them for sex while in the Dominican Republic later recanted their allegations, claiming they had been paid to make the accusations.

Yet a new ad from Mr. Hugin repeats the allegations as uncontested facts. While the federal government charged in a court document during Mr. Menendez’s trial that “the Government took responsible steps to investigate these serious criminal allegations, which were not so ‘easily disprovable,’ as the defendants suggest,” the Hugin ad takes liberties with the unsubstantiated allegations.

“What about the underage girls who accused you, according to the F.B.I.?”

This is misleading.

The allegations were made by an anonymous tipster who called himself Pete Williams, a wry reference to a former senator from New Jersey, Harrison “Pete” Williams, who was convicted in 1981 of taking bribes. The tipster first reached out to Citizens for Responsibility and Ethics in Washington, a left-leaning legal watchdog group . The group eventually passed the allegations to the F.B.I.

The ad refers to an F.B.I. affidavit filed to show probable cause for a search warrant . In the affidavit, Special Agent Gregory J. Sheehy, recounts his attempts to investigate the tipster’s allegations.

As of the writing of this Amended Affidavit, Mr. Williams has refused to meet with the F.B.I., either by phone or in person. Mr. Williams has not disclosed enough information for the F.B.I. to identify any minors.

“President Obama’s Justice Department had evidence that for several years Menendez had been traveling to the Dominican Republic to engage in sexual activity with prostitutes, some of whom were minors.”

This is misleading.

This part turns on a very loose use of the phrase “had evidence.”

According to the affidavit, Mr. Sheehy attempted to corroborate the allegations. He is able to confirm that Mr. Menendez had been in the Dominican Republican at the same time as one unidentified woman who, through the tipster, said she had sex with Mr. Menendez.