Senior Republican Senator Lindsey Graham blocked a resolution that would have formally recognised as genocide the mass killing of the Armenians by the Ottoman Empire from 1915 after meeting Turkish President Recep Tayyip Erdoğan.

The U.S. House of Representatives last month passed a similar resolution by 405 votes to 11 amid growing anger in Washington over Turkey's military operation against Kurdish forces in northern Syria.

Democrat Senator Robert Menendez asked for consent to pass a resolution that would have provided "official recognition and remembrance" of the Armenian genocide, the Hill said.

"We cannot turn our backs on the Armenian victims of genocide," he said, adding that he had listened to Erdoğan's comments on the issue during a press conference with President Donald Trump at the White House.

Erdoğan said: "The decision makers in an incident that took place about 104 years ago should not be politicians, but historians. I believe the Senate will take this - take the United States out of this vicious cycle, which happened as a result of the resolution of the House of Representatives."

Graham objected to passing the resolution in the Senate, saying senators shouldn't "sugarcoat history or try to rewrite it," according to the Hill.

Graham, who was a harsh critic of Ankara's incursion into Syria, took part in a White House meeting with Erdoğan, Trump and a group of Republican 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 said.

U.S. based Armenian organisations gathered at Lafayette Park across the White House on Wednesday to protest Erdoğan-Trump meeting.