The talks in Maryland are an attempt to relaunch peace negotiations between the Israel and the Palestinian administration after they broke down seven years ago.
Abbas and Peres were in Ankara to establish an industrial park in the West Bank, which will be sponsored by Turkey - a project expected to generate jobs for thousands of Palestinians.
The two leaders are also due to address Turkey's parliament separately, with both leaders becoming the first presidents of Israel and the Palestinians to address the legislature in Ankara.
"Never before has an Israeli president been in [the Turkish parliament] and the fact that this is happening is a signal by Turkey of the neutral platform that it can extend in terms of this highly divided region," Mike Hanna, Al Jazeera's correspondent in Istanbul, said.
Peres on Monday welcomed the participation of all "moderate countries" in the Annapolis conference.
He said "the voice of peace will be stronger and louder" with more participants attending, but he said Syria had not worked towards achieving peace.
Imad Moustapha, Syria's ambassador to the US, last week called the talks a "waste" and a "photo opportunity".
Turkey, Israel's closest ally in the Islamic world, has in the past played the role of mediator between the Jewish state and its Muslim neighbours.