FRANKLIN LAKES, N.J. — Senator Robert Menendez spoke in a level, matter-of-fact tone, but his words were grave. Anti-Semitism is on the march around the world, he said. Negotiations with Iran, he warned, have reached “the witching hour,” with the security of both the United States and Israel at stake.

Addressing a Sunday morning crowd at the Barnert Temple, a Reform synagogue in northern New Jersey, Mr. Menendez promised that his listeners could count on him to be vigilant.

“There can be no denying the Jewish people their legitimate right to live in peace and security,” he said, vowing just days before the Passover holiday that he would stand with Israel “so long as I have a voice and a vote in the United States Senate.”

It was the closest the senator came to acknowledging his recent troubles. For weeks, Mr. Menendez, a New Jersey Democrat, has battled to keep his standing in the Senate amid an unfolding investigation into his relationship with a political benefactor, the Florida eye surgeon Salomon Melgen, and whether Mr. Menendez improperly influenced policy on his behalf.