Heading into the meeting, Barak warned it would take time to get diplomacy back on track, reports CBS News Correspondent Jesse Schulman.
Although there seemed to be little substance, Palestinian officials described the session as a good start, while Israeli analysts said the meeting achieved its key goal of breaking the ice that had piled up during the years of Israel's previous, hard-line government.
There was no clear answer from Arafat to Barak's main proposal, however -- postponing implementation of parts of the Wye land-for-security accord until the sides begin negotiations on the final status of Palestinian areas.
Heading into the talks, Palestinian officials had insisted upon full and immediate compliance with signed agreements, including the Wye River land-for-security accord, which calls for Israeli withdrawal from West Bank lands.
But Arafat said at one point in the talks: Â"We believe that we need to do both, implement Wye and move to final status negotiations.Â"
The session at a border crossing between Israel and the Gaza Strip lasted little over an hour. The two leaders -- Barak in a dark suit, Arafat in his trademark fatigues -- shook hands and waved to onlookers as they entered the meeting room.
It was the first face-to-face talk by Israeli and Palestinian leaders since December, and Barak's first meeting with Arafat since the Israeli leader was sworn in five days earlier.
A former army chief of staff, Barak won election two months ago on a platform of reviving the peace process. Palestinians said enough time had already been lost during the long deadlock under his predecessor, Benjamin Netanyahu.
Barak sought to dampen expectations about timing.
"The diplomatic road will not be short," he told a Cabinet meeting -- his first -- hours before the summit. He briefed ministers on talks Friday with Egypt's President Hosni Mubarak and upcoming meetings with Jordan's King Abdullah II and President Clinton, the Cabinet said in a statement.
Barak won a pledge from Arafat to follow a Â"zero toleranceÂ" policy toward terrorism, an issue that was crucial in Sunday's talks.
But in Gaza, the spiritual leader of the radical Islamic group Hamas, which has carried out suicide attacks in the past that killed scores of Israelis, urged Arafat to "put a halt to constant Palestinian concessions in the face of Israeli piracy.
"We are still under occupation, and when you live under occupation, no one should expect you to surrender," Sheik Ahmed Yassin told reporters. "That is why we won't change our strategy of resistance."
Israeli observers acknowledge that Arafat hs clamped down on the Islamic militants in recent months. It was recognized that if there had been bombings or other attacks during the Israeli election campaign, Barak's chances of defeating Netanyahu would have been badly jeopardized. During the 1996 election campaign, a series of bombings in Israeli cities helped propel Netanyahu to victory.
Arafat also brought up the Palestinian demand of putting a stop to Jewish settlement activities in the disputed areas.
Barak limited himself to a promise not to build new settlements and not to dismantle existing ones.
Â"I have no illusions and I believe the chairman (Arafat) has no illusions that we are going into tough negotiations with many ups and downs,Â" Barak said.
Barak's cramped schedule in the coming days includes Tuesday's summit with Jordan's King Abdullah II in the Jordanian port of Aqaba and a weekend trip to Washington, where he is to confer with President Clinton, top administration officials and Congress members.