President George W. Bush, poised to finish his presidency without the Middle East peace deal he once said was in reach, declared Friday that Israelis and Palestinians have made great strides toward settling decades of conflict.

"No question, this is a hard challenge," Bush said in the Oval Office alongside the Palestinian leader, Mahmoud Abbas. "But nevertheless, people must recognize that we have made a good deal of progress."

Abbas concurred: "Some might say that all these efforts perhaps went in vain. I happen to disagree."

In what was likely their last face-to-face meeting before Bush leaves office on Jan. 20, the two men sought to praise each other and emphasize what has been gained, not the opportunity lost. Their meeting came just days after the UN Security Council endorsed as irreversible the administration's peace process. It was launched by Bush last year in nearby Annapolis, Maryland, and championed by Abbas and outgoing Israeli Prime Minister Ehud Olmert.

The president seized on the UN move as confirming a path to a Palestinian state, and a path to peace in the Middle East.

Bush had said confidently that a peace deal, built around the outlines of a first-ever Palestinian state living in peace with Israel, was doable by year's end.

But continuing violence, the situation in Gaza, which is controlled by the militant group Hamas, and internal political developments in Israel have made the deadline unreachable. So instead, the Bush administration has tried to lock in the Annapolis process by enshrining it in the international system.

For his part, Abbas was effusive about Bush's efforts. He said the U.S. president was fair and firm in pushing both sides to meet their obligations.

"There is no doubt that we will always remember the efforts that you have undertook to promote the peace process," Abbas said.

He also reaffirmed the Palestinian commitment to the peace talks, and not as a slogan or a rhetorical commitment. We are practically committed to the peace process. And we are confident all these efforts will be transferred to the new administration.

He was referring to Democrat Barack Obama, who succeeds Bush on Jan. 20.

In the Middle East, meanwhile, more reminders arose of the fragility of the existing peace. Hamas formally announced on Friday the end of its unwritten, often-breached truce with Israel as Palestinian militants in the Gaza Strip fired four rockets into southern Israel.

The Israeli military said two rockets were fired Friday morning and two more after sunset. It said troops guarding Israeli farmers in fields adjoining Gaza also came under sniper fire from across the border. No injuries were reported in any of the incidents.

In a statement posted on its Web site, Hamas said Israel had breached agreements by imposing a painful economic blockade on Gaza, staging military strikes into the densely populated coastal strip and continuing to hunt down Hamas operatives in the West Bank.

Hamas, which violently seized control of the Gaza Strip in June 2007, is listed as a terrorist organization by Israel, the United States and much of the world, and Israel has no official direct contacts with it.

In Washington, Secretary of State Condoleezza Rice was critical of Hamas' move.

"I sincerely hope that there will not be a resumption of the violence, because that is not going to help the people of Gaza, it is not going to help the Palestinians, it is not going to help the Palestinian cause," she said.