Sen. Robert Menendez (D-N.J.). (MANDEL NGAN/AFP/Getty Images)

Sen. Robert Menendez (D-N.J.) said in a CNN interview Tuesday that he would not be surprised if the Cuban government plotted against him and called the possibility "appalling" as he urged federal investigators to probe the matter.

The Washington Post's Carol D. Leonnig and Manuel Roig-Franzia reported Monday that Menendez's attorney wrote a letter to the Justice Department asking for an examination of evidence the Cuban government plotted to smear the senator with allegations he partied with underage prostitutes.

Menendez, a Cuban American, wouldn't comment on his lawyer's communications with the Justice Department in the television interview. But he told CNN's Dana Bash the possibility of a Cuban plot to sully his image "is something that should be investigated by the Justice Department and others," adding that it "wouldn't surprise" him if the Cuban government tried to go after him.

"I think it should be pretty appalling that a foreign government would be engaged in trying to affect an election," Menendez said. He added, "If that can happen, I think there are real consequences for our democracy."

When asked he if had proof the Cuban government targeted him, Menendez sought to shift attention to the U.S. federal government, which he said needs to review available evidence in its possession.

Menendez dismissed the possibility that he or his team leaked his lawyer's letter to distract from the investigation into whether he used his position to benefit the interests of a friend and donor.

"I think that's pretty far-fetched idea​," said the senator.