The woman, 23-year-old Nexis de los Santos, asked the court to block any possible arrest for making statements she now says are false: accusing the senator and several associates of using prostitutes in the Dominican Republic.
Judge Ismael Ramirez, at a hearing in the town of La Romana, determined he did not have enough information and ordered the testimony of New Jersey Sen. Robert Menendez and Salomon Melgen, a Florida eye doctor and major campaign contributor.
Neither man would be required to appear personally before the court and could send an attorney to the hearing, scheduled for June 10, prosecutor Jose Polanco said after the hearing.
Tricia Enright, a Menendez spokeswoman, said the senator does not plan to attend any hearing.
"We certainly hope the appropriate authorities are able to get to the bottom of who has been behind this smear campaign," she said.
De los Santos, who did not attend the hearing in La Romana, has said she has been receiving anonymous threatening phone calls warning her not to reveal what she says is the truth: that she was paid by an attorney to claim she had sex with the men. Polanco said his office is investigating the reported threats.
The woman's attorney gave the court an affidavit saying that she was one of the women interviewed in a video published on a Washington-based website, The Daily Caller, alleging that they had been paid to have sex with Menendez and Melgen, including at a point when she was underage. De los Santos says in her affidavit that she has never met either man and was paid to read a script on the video by a Dominican attorney, Melaneo Figueroa.
On its website early Tuesday, The Daily Caller said neither of the women in the video identified herself as Nexis de los Santos. The website also said both women consented to the presence of a video webcam.
Polanco said he is seeking to interview Figueroa but has not located him. The attorney has not responded to repeated phone calls and visits to his office.
Sen. Menendez has maintained all along that he never paid prostitutes for sex and said he is looking forward to whatever evidence emerges from courts in the Dominican Republic to vindicate him.
"I've always said that these are false, they're smears," Menendez, D-N.J., told reporters Monday at the Capitol. "And, so, I look forward to seeing whatever the Dominican courts have that prove what I've said all along."
De los Santos is seeking legal protection because she fears she might be prosecuted for making false statements in the video.
Copyright 2013 The Associated Press.