Graham objected to passing the resolution in the Senate, saying senators shouldn’t “sugarcoat history or try to rewrite it.”
Under the Senate’s rules, any one senator can ask for consent to pass a bill or resolution, but any one senator can block it.
Graham’s objection came hours after he took part in a White House meeting with Trump, Erdoğan and a group of GOP senators.
“I just met with President Erdoğan and President Trump about the problems we face in Syria by the military incursion by Turkey. I do hope that Turkey and Armenia can come together and deal with this problem,” he added on the Senate floor.
Graham added that he was objecting “not because of the past but because of the future.”
The resolution passed the House in a 405-11 vote. Turkey does not recognize the killing of 1.5 million Armenians as genocide.
The House vote came in the wake of Ankara’s military incursion into northern Syria after the Trump administration pulled troops from the area.