Weeks before traveling to Israel, President Bush yesterday expressed confidence that an agreement over the “definition” of a Palestinian Arab state will be made prior to the end of his administration.

Next month Mr. Bush plans to attend the celebration of the 60th anniversary of the May 15, 1948, declaration of an independent Jewish state, long seen by Arabs as a “naqba,” or “catastrophe.” Hosting President Abbas yesterday at the White House, he said the quest for the creation of a Palestinian Arab state is a “high priority” for his administration. But as Mr. Abbas was in Washington, a spokesman for his chief rival, the terrorist organization Hamas, made a dramatic announcement in Cairo, offering a 6-month cease-fire in Gaza. There was no immediate Israeli response.

Israel and America have refused to negotiate directly with Hamas. Yesterday’s announcement by the top Hamas official, Mahmoud A-Zahar, followed meetings in Damascus last week between President Carter and top Hamas leaders that were denounced in Jerusalem and Washington. Israel’s ambassador to the United Nations, Dan Gillerman, yesterday said he believed Mr. Carter was “a bigot,” and someone “who went to the region with soiled hands and came back with bloody hands.”

In recent talks steered by Washington, Mr. Abbas and Israeli Prime Minister Olmert reportedly tried to reach a “shelf agreement” that would define borders, but defer other sticking points for later. Mr. Bush’s critics argued it was no more than an attempt to create a diplomatic legacy.

I “believe strongly that when history looks back at this moment and a state is defined, that the Palestinian people will thank you for your leadership,” Mr. Bush told Mr. Abbas yesterday. “I’m confident we can achieve the definition of a state.” But he acknowledged that even the modest goal of defining a state “that doesn’t look like Swiss cheese,” would require hard work.

Mr. Abbas highlighted Mr. Bush’s role as peacemaker and praised the so-called “Arab initiative,” which, he said, “simply states that peace would be achieved after the Israeli withdrawal from the occupied Arab and Palestinian territories.” But the plan adopted by the Arab League also calls for Arab sovereignty over Jerusalem and the right of descendents of refugees to “return” to Israel.

“The problem isn’t the definition of a state, we all know what that is,” said a former Israeli deputy security adviser, Chuck Freilich, currently at Harvard. Rather than the borders of the Palestinian Arab state, he added, the stumbling blocks for a comprehensive agreement are questions relating to the status of Jerusalem and refugees, which may be deferred to five years after the proposed shelf agreement is signed. “We don’t need another ceremony,” he said. “If it is no more than a show, it will strengthen Hamas.”