In a second phase, the Arab diplomats said, the Palestinian Authority would take more concrete steps to disarm Hamas and other militant groups, once Israeli restraint was established.
When he met Mr. Sharon at the White House on Sunday, Mr. Bush had notably omitted any call for Israeli restraint, according to administration officials.
Before tonight's Israeli raids, the Jordanian prime minister, Ali Abu al-Ragheb, had urged Israeli restraint, warning that any retaliation would only lead to a vicious cycle of bloodshed.
"There's an attempt to signal that Israeli restraint now is not being purchased at the price of foresaking our interest in pushing along the peace process later," an official said.
His barbarous Scud attacks on Israeli cities were thwarted by Patriot rockets, urgent U.S. diplomacy and anguished Israeli restraint.
Mr. Clinton's appeals for Israeli restraint and concessions were more muffled.
Several rightist legislators attacked Mr. Barak for what they termed the Israeli Army's excessive restraint in the face of Palestinian provocation.
He portrays the daily clashes between rioters and soldiers at the crossroads between Beit El and Ramallah as an example of laudable Israeli restraint.
And 59 percent said they supported Israeli military restraint.
Along with much of the world, Mr. Bush urges Israeli restraint.