While the right wing backs his effort to end the violence, it would not support him if he took extra steps to revive the peace effort.
Even before an agreement was reached tonight to revive the frozen peace effort, a senior Palestinian negotiator, Saeb Erekat, acknowledged that the dynamics of the dialogue had changed for the better.
The death of Mr. Arafat is viewed as an opportunity to revive the moribund Israeli-Palestinian peace effort.
The two steps represented a slight swiveling toward each other as the Israelis and the Palestinians work with President Clinton to try to find a way to revive the moribund peace effort.
Yet another attempt to revive the peace effort with Syria collapsed this spring after Mr. Clinton had a failed meeting with Mr. Assad in Geneva.
And they acknowledged that reviving the peace effort would be a near impossibility in the administration's remaining time.
But Mr. Abbas appeared to be motivated mostly by a decision that a rude jolt was needed to revive the peace effort.
By the end of their ride together, they concluded that Washington had to move more forcefully to revive the peace effort with a package of American ideas.
The prospect of a meeting should put added pressure on the leaders to revive the peace effort, American officials said.
A Syria detached from Iran and engaged by the United States could conceivably be enlisted in reviving the Arab-Israeli peace effort and containing the spreading chaos in Iraq.