WASHINGTON – Federal prosecutors said Monday that they aren’t convinced claims U.S. Sen. Robert Menendez cavorted with underage hookers – widely seen as discredited – are false.

Lawyers for the New Jersey Democrat last week asked a federal judge to dismiss charges that the senator took bribes from a Florida eye doctor, Salomon Melgen, and in exchange used his power to do business and personal favors for him.

The defense said the case is bogus because it sprang from “easily disprovable” claims that Menendez slept with underage prostitutes while hosted by Melgen at a Dominican Republic villa.

Three women who made the prostitution allegations later recanted and said they were paid to level the charges. Neither Melgen nor Menendez was charged with soliciting underage prostitutes.

But in a motion Monday asking the judge to ignore the defense arguments, Justice Department lawyers say the hooker allegations “were not so easily disprovable as the defendants suggest.”

Prosecutors used the defense claims to highlight previously undisclosed tidbits on Menendez’s pursuit of younger woman.

The lawyers say their investigation resulted from “specific, corroborated allegations that defendants Menendez and Melgen had sex with underage prostitutes in the Dominican Republic.”

Menendez’s camp said Monday that the Justice Department filing is a smear tactic designed to use the exchange of motions to dump dirt on the senator.

“The filing today shows that the Department of Justice tried to make up for weak allegations about public corruption by soliciting allegations about sex,” said Menendez spokesman Steven Sandberg. “They continue that refrain now with new salacious allegations, again having nothing to do with the actual charges in the case.”

“There is not one interview, paper, email or grand jury witness-not a shred of any evidence-that says Senator Menendez was involved in any prostitution, let alone underage women,” Sandberg said. “Period. And the government knows it.”

The filing discloses circumstantial information indirectly linking Menendez to prostitutes.

The prosecutors noted eyewitness testimony that Melgen, 61, attended a party that included prostitutes, and that he flew “numerous young women” to the Dominican Republic on his private jet.

“Many of these young women receive substantial financial support from defendant Melgen,” prosecutors say.

Melgen flew two strippers he met at a South Florida “Gentleman’s Club” to his villa after paying them a combined $3,000, the government says.

A pilot described a series of “young girls” who “look like escorts” on Melgen’s plane, prosecutors wrote.

“Some of the young women who received substantial sums of money from defendant Melgen were in the same place as defendant Menendez at the same times,” the government notes.

Prosecutors say that when the allegations about hookers surfaced, Menendez lied, making the “demonstrably false” claim that he’d only flown on Melgen’s plane three times.

Menendez’s defense complained that prosecutors “flooded the grand jury proceedings with inflammatory questions regarding sexual relationships, affairs, lavish gifts which are unrelated” to the charges he faces.

But prosecutors said they “did not interview or subpoena all of” Melgen or Menendez’s girlfriends.

They called only those who were involved in the corrupt exchange where Menendez used his power to help “Melgen bring his foreign girlfriends into the United States,” while Melgen used his wealth to help “Menendez take his American girlfriends on exotic overseas vacations.”

To Menendez’s claim that they went out of their way to imply he had an improper relationship with a female staffer, prosecutors noted the aide stayed with Menendez at Melgen’s villa twice, and flew there with the senator on Melgen’s jet.

Those are flights “Menendez did not pay for or report, and continued to conceal after the allegations surfaced,” prosecutors said.