WASHINGTON — The Senate voted unanimously on Thursday to recognize the Armenian genocide as a matter of American foreign policy, a move that was made over the objections of the Trump administration and that underscored lawmakers’ bipartisan rage at Turkey.

The passage of the legislation, a symbolic victory for Armenians around the world, is the first time Congress has formally designated the 1915 mass killings of an estimated 1.5 million Armenians at the hands of the Ottoman Empire as a genocide.

“To overlook human suffering is not who we are as a people,” a visibly emotional Senator Robert Menendez of New Jersey, the top Democrat on the Foreign Relations Committee, said on the Senate floor moments after the legislation passed. “It is not what we stand for as a nation. We are better than that, and our foreign policy should always reflect this.”

Mr. Menendez and his Republican co-sponsor, Senator Ted Cruz of Texas, had tried for three consecutive weeks to force passage of the measure after the House approved it in October. Each time, they were blocked by a Republican senator who, at the behest of the White House, argued that such a resolution would damage the United States-Turkey relationship.

On Thursday, no one rose to object.

“Many of the arguments the administration had raised were arguments of timing, that the administration thought it wasn’t the right time to pass the resolution,” Mr. Cruz said in a brief interview. “Each time an individual senator raised the objection, that senator said they would not do so again. So I’m glad today no one chose to object.”

The move has incensed Turkey, a NATO ally that has steadfastly denied that the atrocities amounted to genocide. For years lawmakers sidestepped endorsing such a resolution to preserve the United States’ relationship with Ankara.

But ties between the countries have become strained. Outraged by President Recep Tayyip Erdogan’s incursion into northern Syria in October and his purchase of a Russian missile defense system, the Foreign Relations Committee mobilized this week to advance a package of sanctions targeting Turkey.

Senator Jim Risch, Republican of Idaho and the panel’s chairman, had previously held back from pushing the legislation forward. But on Wednesday, he said that Turkey had “thumbed their noses at us.”

“If we just look the other way on this,” Mr. Risch said, “we will be viewed as weak.”

A bipartisan group of lawmakers in the Senate and the House also agreed to include in a must-pass annual defense bill a provision cutting off the transfer of F-35 fighter jets to Turkey over its purchase of the antimissile system.

“History will note these resolutions as irresponsible and irrational actions by some members of the US Congress against Turkey,” Fahrettin Altun, Mr. Erdogan’s communications director, said on Twitter of the sanctions bill and the Armenian genocide resolution. “They will go down in history as the responsible party for causing a long lasting damage between two nations.”

The Senate’s vote on Thursday, while ultimately a symbolic message, amounted to an additional sprinkling of salt in Turkey’s wound. But it meant much more to Armenian-American activists who for years lobbied for Congress to officially recognize the mass killings as an act of genocide.

“With this action, the Senate joins the House and its overwhelming vote upholding the proud American record of recognition and condemnation of the Armenian genocide,” said Bryan Ardouny, the executive director of the Armenian Assembly of America. “The Congress of the United States of America has spoken.”