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"No question, this is a hard challenge. But nevertheless, people must recognize that we have made a good deal of progress," Bush told reporters following the meeting.
"I was pleased to note that the UN Security Council passed a resolution which confirms that the bilateral negotiation process is irreversible and it's a path to a Palestinian state and a path to peace in the Middle East," he said.
In response, Abbas said that the Palestinian Authorities will stick with the peace process. "There is no doubt that we will continue these efforts and the peace negotiations," he said.
"We are practically committed to the peace process, and we are confident all these efforts will be transferred to the next (Obama)administration."
It was generally believed that the summit meeting was a farewell one, during which the two leaders focused on the status of Middle East peace efforts since Israeli-Palestinian talks were relaunched at a conference in Annapolis, Maryland in November 2007.
Prior to the meeting, U.S. Secretary of State Condoleezza Rice had talks with Abbas on Thursday. "The secretary has committed to continue to work on this process" until President-elect Barack Obama and his team take over on Jan. 20, State Department spokesman Sean McCormack said.
In November 2007, Bush convened a summit of Palestinian Authorities and Israeli leaders in Annapolis to launch a new round of peace talks.
However, the White House announced early last month that there will be no Middle East peace pact on President Bush's watch due to disagreements on the most divisive issues and escalating violence in the region.