The rejection of the proposal was particularly politically damaging for the hard-line interior minister, Nicolas Sarkozy, who had expected a victory.
Last week, the hard-line interior minister, Nicolas Sarkozy, postponed a trip to the French West Indies, rather than face an expected protest of the vote.
Mr. Barak is unlikely to travel to Washington with his most hard-line ministers because they are expected to quit before he leaves.
It was closed, but Israeli reports said several hard-line ministers revived demands that Mr. Arafat be expelled to Gaza or abroad.
Meanwhile, Israel's cabinet on Sunday overwhelmingly rejected a proposal by hard-line ministers to postpone the Gaza withdrawal until November.
In recent weeks, Palestinian leaders have been debating whether to call a cease-fire, in part to strengthen the opponents of Israel's hard-line prime minister, Ariel Sharon.
The resulting scandal led to the resignations of Greece's hard-line foreign minister and several intelligence officers who were considered strongly anti-Turkish.
Just today, despite the official cease-fire, guerrillas were accused of blowing up a motel, killing two people, in Celopek, the hometown of the nation's hard-line interior minister.
What Hamas is willing to accept is not likely to please Israel's hard-line prime minister, Ariel Sharon.
The new structure has been tested by what has seemed like an internal struggle between more reform-minded and more hard-line ministers.