TEL AVIV, Israel – President Bush called Prime Minister-Elect Olmert yesterday, congratulating him on his election victory and signaling that both Washington and Jerusalem are interested in maintaining the close relations that were formed between Mr. Bush and Prime Minister Sharon.

The increasingly strong American-Israeli relationship is admired by Israelis who at times see Washington as their ally in a hostile world that includes an ever more hostile Europe. But the relationship, which is built on mutual interest, might have unexpectedly influenced Tuesday’s elections, when some Israelis were lulled into believing that peace and security issues are no longer in their hands – and that decisions are made in faraway places like Washington.

According to a statement released by Mr. Olmert’s office, Mr. Bush invited the victorious candidate to visit the White House as soon as he completed composing his coalition government. Mr. Olmert said he “is interested in continuing the same policy begun by Prime Minister Sharon and to advance the diplomatic track,” the statement said.

American officials also have sent e-mails to diplomats in the region, instructing them not to have any connection with the Hamas government that was sworn in yesterday by the Palestinian Authority’s leader Mahmoud Abbas, according to the State Department Spokesman Sean McCormack.

“If the goal of the United States is two states living side by side in peace and one government elected says, ‘We want to destroy one of the parties,’ it makes no sense for us to support that government,” Mr. Bush said in Washington yesterday.

In what Israeli analysts describe as his first real test as acting prime minister since Mr. Sharon’s stroke in January, Mr. Olmert, along with Foreign Minister Tzipi Livni, quietly convinced American and some European policymakers to impose a freeze on Hamas officials as soon as the new Hamas-led government is sworn in.

An assistant secretary of state for Near Eastern affairs, David Welch, and the deputy director of the National Security Council, Elliott Abrams, were scheduled to arrive in Israel last night for what one Israeli foreign office official described as a “routine” round of talks about the new realities, including the Hamas-led government.

According to some right-wing critics of Mr. Sharon, this was the type of routine consultation between Washington and Israel that led to the Gaza withdrawal, a notion that a former Israeli Defense Minister and ambassador in Washington, Moshe Arens, scoffs at. “There is a myth about constant White House pressures on Israel,” he told The New York Sun yesterday.

Mr. Arens, a strong critic of Mr. Sharon’s Gaza withdrawal as well as Mr. Olmert’s plan for future disengagement, noted that it was Mr. Sharon who suggested the Gaza withdrawal plan to Washington, not the other way around. “The American president who will oppose any Israeli withdrawal is yet to be born,” he said.

“Our common interests have increased each year for the last few decades,” a senior fellow at the Shalem Center, Dan Schueftan, said.

But this view is not shared by all Israelis. And their ambivalence toward America might explain how Tuesday’s election was fought mostly on issues that had little to do with security and peace, which have dominated past campaigns.

Unlike the fear on the right that American pressure might lead to compromise on national security, some on the left believe that big decisions are made far away, in Washington, or as part of a global strategy that Israel does not really influence.

“Condi decides all those things anyway, so it’s time for us to worry about the less fortunate,” one Tel Aviv beachgoer said on Tuesday, before voting for the Pensioners Party. The party surprised most election analysts by attracting many young supporters. It gained seven seats in the 120-member Knesset, making the upstart party a very likely candidate to join Mr. Olmert’s coalition.

Pensioners Party leader, former Mossad agent Rafi Eitan, was the man who controlled convicted spy Jonathan Pollard, and has since been barred from visiting America. The affair has created friction between Washington and Israel.

“The Americans do not forget,” Mr. Schueftan said, adding that it was “ironic” that the defense secretary at the time of the Pollard affair, Caspar Weinberger, passed away the same day Mr. Eitan was elected to the Knesset.

This might become the first time an Israeli Cabinet minister is fugitive wanted by Washington, noted one of Israel’s leading columnists, Nahum Barnea. “This might not be all that pleasant,” Mr. Barnea wrote in the daily Yediot Achronot yesterday, “but it’s not a catastrophe either.”