Armenia estimates that 1.5 million people were killed
Barack Obama's words on the day marking the killing of Armenians by Turks in World War I were "unacceptable", Turkey's foreign ministry has said.
Though Mr Obama did not use "genocide", as he did during his election campaign, Ankara said he failed to honour those Turks killed by Armenians at the time.
"Everyone's pain must be shared," President Abdullah Gul of Turkey said.
President Obama described the deaths of the Armenians as "one of the great atrocities of the 20th Century".
He appealed for Turks and Armenians to "address the facts of the past as a part of their efforts to move forward".
The two countries agreed this week on a roadmap for normalising relations.
While admitting many Armenians were killed, Turkey, a Nato member and key American ally in the Muslim world, denies committing genocide, saying the deaths resulted from wartime fighting.
Armenia has long campaigned for the loss of its people to be recognised as a crime of genocide and it commemorated the event with ceremonies on Friday.
'My view unchanged'
"I have consistently stated my own view of what occurred in 1915, and my view of that history has not changed," Mr Obama said in a written statement.
"My interest remains the achievement of a full, frank and just acknowledgment of the facts."
In a January 2008 statement on his campaign website, Mr Obama wrote: "The Armenian genocide is not an allegation, a personal opinion or a point of view, but rather a widely documented fact supported by an overwhelming body of historical evidence."
"America deserves a leader who speaks truthfully about the Armenian genocide and responds forcefully to all genocides," the 2008 statement added.
On Friday, he said the Armenians killed in the final days of the Ottoman Empire "must live on in our memories".
"I strongly support efforts by the Turkish and Armenian people to work through this painful history in a way that is honest, open, and constructive," he added.
That part of the Obama statement was considered positive by Turkey, a key US ally in the region.
But "history can be construed and evaluated only on the basis of undisputed evidence and documentation," Turkey's foreign ministry statement said.