Mr. Obama has hailed the steps taken by Turkish and Armenian leaders to resolve their differences as "historic and courageous."
During his address to Turkey's parliament Monday, the U.S. leader said he supports full normalization of relations between the neighbor states. He added that an open border would return people of both nations to "a peaceful and prosperous coexistence."
Earlier, a reporter reminded Mr. Obama that he had called for Turkey to acknowledge the early 20th-century killing of Armenians by Ottoman Turks was genocide and asked if his position still stood. The U.S. president said he had not changed his view, but said the issue is a matter best resolved by the two nations involved, without outside interference.
Turkey strongly rejects the assertion that the Armenians in Turkey were victims of genocide. Turkish President Abdullah Gul said he welcomes international participation in a joint commission of inquiry on the subject, and pledged to accept the findings of such a review.
Mr. Obama said all democracies must face the issue of how to deal with the past. He said the United States is still working through its "darker periods" of slavery, and of ill treatment of Native Americans.
The U.S. president called on Turkey to play "a constructive role" in resolving the conflict in Nagorno-Karabakh, an ethnic Armenian enclave in Azerbaijan. Turkey broke relations with Armenia over the dispute, which is not yet settled, 15 years after open warfare in the enclave ended.
Mr. Obama paid tribute to Turkey, saying it is poised to be the only country in the region to have normal and peaceful relations with all of the South Caucasus nations.