That marked the third time a Republican senator blocked the measure at the White House's request.
The resolution does not require President Trump's signature, because it is nonbinding. But Republican senators had blocked a vote in the Senate since the Erdogan meeting. Each time, a Republican senator objected, citing disapproval of the motion by the White House.
After the House passed a broader Turkey sanctions bill 403-16 in October, Senate Majority Leader Mitch McConnell, R-Ky., indicated that he would not put the legislation on the floor, arguing that it was too broad and unlikely to alter Ankara's behavior.
Last month, Republican Senator Lindsey Graham objected to passing the resolution after Menendez sought consent to pass it.
Azerbaijan threw its support behind Turkey on Friday, criticizing a USA resolution that formally recognized Armenian claims of 1915 events. Since then lawmakers have deferred to presidents of both parties and avoided putting various Armenian genocide resolutions on the floor for fear of upsetting Turkey. Many scholars see it as the 20th century's first genocide.
The designation as a genocide by Congress is a significant political development as Turkey maintains to this day the killings did not constitute genocide and disputes the death toll, putting the figure closer to 300,000.
This resolution's passage comes a day after a Senate committee advanced a sanctions bill aimed at Turkey for its military offensive against Kurdish forces in Syria in October and its recent purchase of the S-400 missile system from Russian Federation.
Ankara lobbied for years against USA recognition of the killings as genocide, and Turkish President Recep Tayyip Erdogan has said he will not recognize the congressional resolution.
"In every previous attempt to politicize history by some members of the US Congress, we reiterated our position to form a group to study it", Altun said.
Turkey informed the US about the reasons and aims of its anti-terror operation in northern Syria, Altun recalled, and added that Turkey refuses to compromise its national security "as some US Congress members are uncomfortable".
The White House reportedly did not want the legislation to move ahead as it negotiated with Ankara on sensitive issues, and following a meeting at the White House between Turkish President Tayyip Erdogan and Trump in November.
Ibrahim Kalin, Turkish presidential spokesman said Turkey "strongly condemned and rejected" the measure. The lower house voted for the piece of legislation in late October in response to Turkey's controversial offensive against Kurdish militia in northeastern Syria. The Turkish ambassador to the United States, Serdar Kilic, warned Congress of permanent "negative resentment" between the two North Atlantic Treaty Organisation allies shortly before the Syria offensive prompted House leadership to put the Armenian genocide resolution on the floor.
And while Trump booted Ankara from the F-35 co-production program earlier this year over its purchase of the Russian-made S-400 missile defense system, the defense bill permanently bans the transfer of the fighter jets to Turkey until it ditches the Russian missile system.