Barak, whose trip was delayed after twice reversing his plane's course due to a hijacking crisis at home, offered little hope the meeting could help to end the bloodshed that has killed some 200 people in the past six weeks.
The Israeli leader, who arrived after nightfall at Andrews Air Force Base in suburban Maryland and went directly to the White House, looked for Clinton to put heat on Arafat to make a public declaration that the Palestinians should not attack Israeli soldiers and civilians.
But Arafat was defiant at an Islamic summit conference in Qatar, where Saudi Arabia, considered moderate by the United States, joined in a call on Muslim nations to cut any ties with Israel.
Arafat said the Palestinians "are determined more then ever to continue their jihad and the resistance of the occupation."
The violence has shattered what remained of Clinton's hopes for a settlement before his term ends in January.
Clinton had Secretary of State Madeleine Albright; Sandy Berger, his assistant for national security; and U.S. mediator Dennis B. Ross, at his side in the Oval Office. Barak was assisted by close aides Gilad Sher and Danny Yatom, and David Ivry, the Israeli ambassador to Washington.
Clinton and Barak posed for pictures seated in front of a fireplace. They took no questions, and reporters were not permitted to attend the brief picture-taking session.
En route, Yatom told reporters Barak's meeting with Clinton was "very important and critical to the peace process."
He said the three-point agenda was to try to bring violence to an end, to look for ways to cease incitement and to discuss possibilities and options for continuing the peace process.
Arafat, who held discussions Thursday with the president, indicated afterward that he would consider another Middle East summit, with Clinton as host, provided it was well-prepared "to ensure its success." And that, the Palestinian leader said, meant on accord on both Jerusalem and refugees.
Barak has refused to turn over all of East Jerusalem to the Palestinians, as they have insisted, but offered them a larger role in running their daily affairs in Israel's declared capital. He has called a time-out in peacemaking until the violence ends.
As the hijacking ended, Barak's plane reversed course for a second time and headed back for Washington. Barak left Israel on Saturday night before the hijacking began. But at a stopover in London, he decided to return to Israel to deal with the crisis. He was still in the air as the hijacking approached a resolution when he decided to resume his journey to the United States.
Some 200 people, most of them Palestinians but also Israeli soldiers and civilians, have died in six weeks of violence on the West Bank, in Gaza and Israel.
Arafat blamed Barak directly, saying Thursday night after meeting with Clinton that the prime minister had reneged on a promise to withdraw Israeli forces from Palestinian areas. Israel says Arafat is responsible for the continued fighting and has urged him to unequivocally call for a halt to the bloodshed and return to the negotiating table.
The violence continued on Sunday. One Palestinian was killed in a stone-throwing clash near the Erez checkpoint between Israel and Gaza, officials at a hospital said. They said the Israeli army had fired live ammunition.
In Hebron, a gunshot was fired at the convoy of U.N. Human Rights Commissioner Mary Robinson as she toured a Jewish enclave. One bullet hit a car, but no one was hurt. The Israeli army said the shots were fired from Palestinian positions.
Two Egyptians were wounded, one critically, by Israeli gunfire in Gaza, according to Egyptian officials.
In clashes Saturday, six Palestinians and one Israeli soldier were killed on the West Bank and in Gaza.
Clinton has devoted much time and effort on trying to prod Israel and the Palestinians into an accord. In July, he mediated between Arafat and Barak at Camp David, the presidential retreat outside Washington, but could not overcome disputes over Jerusalem's future, refugees, and a handful of other tough issues.
Still eager to attain his goal, Clinton sauid last week he would not apply pressure and that any settlement must spring from the parties themselves.
"I know Clinton as someone who keeps his promises," Yatom said. "I have no doubt he will keep all his promises now."