Prime Minister Olmert, saying it is hard to imagine another American president as friendly to Israel as President Bush has been, told his Cabinet ministers yesterday that they must move on regional diplomacy before the end of Mr. Bush’s term.

Aides to Mr. Olmert quickly sought to dispel any impression that the prime minister doubts Senator McCain’s or Senator Obama’s support for Israel. But as the two presidential candidates compete to distance themselves from Mr. Bush’s record, Mr. Olmert’s remarks underscored Israelis’ affection for the outgoing president.

The Israeli leader, aides said, was seeking to highlight the need to move swiftly to sign agreements with President Abbas of the Palestinian Authority. At the same time, several top Israeli officials hinted that Israel soon would launch an extensive military operation to stop the rocket attacks from Gaza. Mr. Olmert’s Cabinet could decide as early as today whether Israel will mount the operation or agree to an Egyptian-brokered temporary cease-fire with Hamas, which controls Gaza.

“The current situation in Gaza is unsustainable,” a spokesman for Mr. Olmert, Mark Regev, told The New York Sun. “One way or another, it has to end.”

But as what Mr. Olmert called the “moment of decision” on Gaza nears, he also spoke of promoting diplomacy with Mr. Abbas, on the basis of the conference Mr. Bush convened last year at Annapolis, Md. Mr. Olmert has long argued that with Mr. Bush in office, diplomacy will be conducted under conditions favorable to Israel, an aide who spoke on the condition of anonymity said.

“Bush is the friendliest president Israel has had. Ever,” a former Israeli ambassador to Washington, Daniel Ayalon, said. “But this does not mean that the next president would not be as friendly. It is very dangerous for Israelis to be seen as meddling in American politics.”

Opponents of Mr. Obama have pointed to an op-ed Mr. Ayalon wrote several months ago in the Jerusalem Post, in which he argued that the Democratic presumptive nominee’s commitment to Israel had yet to be fleshed out.

“I think he was much more specific last week,” Mr. Ayalon said yesterday, referring to Mr. Obama’s speech to the American Israel Public Affairs Committee conference in Washington. “I am convinced that the next president, whoever he is, will build on foundations laid down by Bush.”

Mr. Bush supported Israel during its incursions into Arab West Bank towns in 2002, its pullout from Gaza in 2005, and its war against Hezbollah in 2006, Mr. Ayalon said. And $10 billion in American loan guarantees in 2003 helped Israel stabilize its economy, he added. He also called a letter Mr. Bush sent to Prime Minister Sharon in April 2004 “historic.”

In the letter, the president said conditions on the ground had changed since the 1967 war — changes that must be reflected in future border agreements. “Just as the 1917 Balfour Declaration raised the concept of a homeland for the Jews in Palestine, and then became the foundation of the 1947 U.N. resolution that divided it to a Jewish and an Arab state, the Bush letter laid the foundation to any future agreement over Israel’s borders,” Mr. Ayalon said. “No American president can now back away from the Bush letter.”