It comes after two PSNI detectives travelled to collect interviews connected to their investigation into the murder of one of the so-called Disappeared, Jean McConville.
A US Court of Appeal ordered that 11 interviews out of 85 be handed over to Northern Irish authorities, after it found a lower court ordered the release of more information than legally required.
In a letter to US Secretary of State John Kerry, the chairman of the Senate Foreign Relations Committee said he was concerned the material's release could threaten the peace process.
Mr Menendez demanded that the State department should vet the interviews to be handed over to determine whether their release would damage relations or counter US interest.
The New Jersey Democrat also said the US should invoke a clause in the Treaty with Britain to allow for the transfer of the interviews only for purposes which the US approves and has given consent to - which would allow the American government to bar the use of the interviews in civil proceedings.
"Our country made a significant diplomatic investment in resolving "The Troubles" in Northern Ireland," Mr Menendez said in the letter.
"It would be a terrible error in judgement if the United States was to not engage now in the due diligence necessary to protest our investment in this hard-won peace."
The letter was published on Boston College campaigner Ed Moloney's website.
He and Mr McIntyre have welcomed the senator's intervention and say they hope to see his requests translated into action.
The men carried out the interviews as part of the 'Belfast Project' which began in 2001 with republican and loyalist paramilitaries to form part of an oral history of the Troubles.
Ex-IRA member Dolours Price was one of the interviewees, and it is claimed the former prisoner discussed the disappearance of Ms McConville.
The mother of ten was abducted and murdered by the IRA in 1972. Her body was recovered more than 30 years later.
The interviews were conducted under the assurance that the tapes would not be made public while the subjects were still alive. Price was found dead at her home in Dublin in January this year.
Former IRA member Brendan Hughes, who also took part in the project, died in 2008.