JERUSALEM — Over the past several years, Prime Minister Benjamin Netanyahu has on several occasions confronted or even undercut President Obama, taking his message directly to the Israel-friendly United States Congress, challenging Mr. Obama’s appeal to the Arab world, and seeming this fall to support his opponent, Mitt Romney.

Mr. Netanyahu woke up Wednesday to find not only that his Republican friend had lost, but also that many Israelis were questioning whether he had risked their collective relationship with Washington.

“This has not been a very good morning for Netanyahu,” a deputy prime minister, Eli Yishai of the religious Shas Party, told journalists in Eilat.

The prime minister, facing his own re-election fight on Jan. 22, did not directly acknowledge any missteps, but he rushed to repair the relationship. He called the American ambassador to his office for a ceremonial hug. He issued a damage-control statement declaring the bond between the two nations “rock solid.” He put out word to leaders of his Likud Party whose congratulatory messages had included criticism of Mr. Obama that they should stop.

Mr. Netanyahu still maintains strong ties to members of Congress, particularly Republicans, and to other influential Americans. But his strained relationship with Mr. Obama may prove more than a temporary political headache. Israeli leaders and analysts are concerned that the prime minister has hampered his ability to influence Washington on vital policy matters, particularly the Iranian nuclear threat and the Israeli-Palestinian conflict. In practical terms, Jerusalem is worried that Washington will agree to direct talks with Tehran, and go easier on the Palestinian Authority’s quest this month for upgraded status in the United Nations.

“Netanyahu backed the wrong horse,” Mitchell Barak, a pollster and strategist, said at a morning gathering of Americans watching the election results here. “Whoever is elected prime minister is going to have to handle the U.S.-Israel relationship, and we all know Netanyahu is not the right guy.”

Mr. Obama’s re-election seemed to embolden Ehud Olmert, the former prime minister who has spent the past few years battling corruption charges, making it more likely that he will forge a comeback that he hopes can unite and expand Israel’s center-left bloc.

“Given what Netanyahu had done these recent months, the question is: Does our prime minister still have a friend in the White House?” Mr. Olmert asked at a meeting with Jewish leaders in New York. “I am not certain of this, and this might be very significant to us at critical points.”

Few believe that Mr. Obama will act to punish Mr. Netanyahu, but their notoriously tense relationship, made worse in recent months not only by the Romney question but also by Mr. Netanyahu’s hard-line position on Iran, could hurt efforts to coordinate priorities. And freed from electoral concerns, the second-term president may prove likelier to pursue his own path without worry about backlash from Washington’s powerful and wealthy pro-Israel lobby.

“I would be surprised if he were more rather than less forthcoming in dealing with Israel,” Bob Zelnick, a former Middle East correspondent for ABC News who now teaches at Boston University, said of Mr. Obama. “My sense is that he both dislikes and distrusts Israeli Prime Minister Netanyahu, and that he is more likely to use his new momentum to settling scores than to settling issues.”

On Iran, the immediate concern here is that a White House pursuit of bilateral talks would stretch out the timetable for diplomacy even as Mr. Netanyahu’s famous “red line” for halting Iran’s capability to develop a nuclear weapon closes in. On Wednesday, one member of the inner circle of Iran’s ruling system said such talks — the subject of an October article in The New York Times — are “not a taboo,” though another said it was a “big mistake” for Washington to think it could “blackmail” Iran into relations.

Several analysts said Mr. Obama was loath to take on a new Middle East military operation; indeed, one of the biggest applause lines in his victory speech was his declaration that “a decade of war is ending.”

Regarding the Palestinians, Israeli officials had been counting on the Obama administration to forcefully oppose the United Nations bid — as it did last year — and to chastise those countries that support it. But Palestinian leaders seemed unworried on Wednesday, making the bid for nonmember state status in the General Assembly a central focus of their congratulations.

“We will not retract,” said Saeb Erekat, the chief Palestinian negotiator. “We hope President Obama will even support this move.”

Regardless of how he handles the United Nations effort, Mr. Obama is unlikely to pursue the peace process more broadly in the early part of his second term, given the turmoil across the Middle East and internal divisions among the Palestinians.

“I think he recognizes the importance of this issue — he would be a fool not to,” said Diana Buttu, a political analyst and former Palestinian Authority official based in Ramallah, in the West Bank. “But when it comes to the priority list of issues he will have to deal with, I’m just not certain that this is going to be No. 1 or even No. 10 on that list.”

Ehud Barak, the defense minister who shared a close partnership with Mr. Netanyahu for much of the last four years but has tried to distinguish himself on Iran and other issues as elections approach, since he leads the separate Independence Party, congratulated Mr. Obama nearly an hour ahead of Mr. Netanyahu, and followed up by e-mailing reporters photographs and video of himself with the newly re-elected president.

“Even if there were certain kinds of bumps on the road in recent years, we should be able to move beyond it,” Mr. Barak said in an interview. “There is nothing better to mend any scar or grudge from the past than making better achievements in the present and the future.”