Authorities in the Dominican Republic want to hear from U.S. Sen. Robert Menendez (D-NJ) and his friend and campaign contributor about a woman's statement that she was paid to falsely claim she had sex with the men.
General Prosecutor Jose Polanco says a court needs testimony from the men or their lawyers before deciding whether to grant the woman's request for a court order barring her arrest for making false statements.
The woman, Nexis de los Santos, submitted an affidavit to the court in La Romana on Tuesday asserting she was paid by a lawyer to record a video saying she had sex with Menendez and Florida doctor Salomon Melgen, which they deny.
She did not appear in court Tuesday and the hearing was postponed until June 10.
The 23-year-old claims she never met Menendez.
The lawmaker has called the allegations "smears."
De los Santos is one of two escorts who had claimed that Menendez used prostitutes while on vacation in the Dominican Republic.
The Associated Press contributed to this report.