Awad said: "This is a commitment for a timetable that we hear for the first time."
He said the three leaders agreed that "the conference gives a large space for optimism".
Meanwhile, Miguel Angel Moratinos, Spain's foreign minister, has said that his country is deploying diplomatic efforts to convince Syria to attend the Annapolis summit.
"Spanish diplomacy is currently working so that Syria is present at Annapolis," he said on Thursday.
The developments come as an Israeli newspaper says that a draft of the joint document that Israel and the Palestinians hope to present at the conference, shows wide gaps.
Israel has avoided mention of issues that have derailed peace talks in the past, including final borders, Jerusalem and Palestinian refugees, the Haaretz said on its website on Thursday.
Dated November 17, and drafted at Jerusalem's King David Hotel, the document came complete with handwritten notes in English and Hebrew penned by negotiators in the margins.
However, many hours of negotiations have followed since that draft was written, and revisions might have been made since that date.
Saeb Erekat, a Palestinian negotiator identified in the report as one of its authors, denied its authenticity but acknowledged that recent negotiations "have run into serious difficulties".
Israel would not comment on the report, though officials did not dispute its authenticity.
Amid the flurry of diplomatic developments, Ismail Haniya, the prime minister of the dismissed Hamas government in the Gaza Strip, has again criticised the Annapolis conference.
"This meeting will be stillborn and will not allow the Palestinian people to win their rights or realise their political aspirations," he said on Thursday.
The previous day, Mahmoud al-Zahar, the former Palestinian foreign minister from Hamas, told Al Jazeera that nothing positive would come from the talks.