One week before a U.N. showdown over Palestinian statehood, the Obama administration is confronting the stark new limits of its influence in the Middle East, including with its chief ally in the region, Israel.

Palestinian President Mahmoud Abbas announced Friday that he will ask the U.N. Security Council next week to approve full membership in the United Nations for a Palestinian state, essentially ignoring warnings from President Obama and other top U.S. officials that the diplomatic clash could further destabilize a region already in political tumult.

“Our choice is the Security Council,” Abbas said in a speech in the West Bank. “As for other options, we will not make a decision on them. We will decide about any other options later.”

Obama, who has promised to veto any such Security Council resolution, had hoped to persuade Israel and the Palestinians to resume peace negotiations as an alternative to the statehood initiative. Israel has said “grave consequences” would follow a Palestinian statehood bid, and U.S. and European diplomats have been scrambling to try to reach a deal that could avert a U.N. vote.

But the U.S. warnings have been ignored, not only by a Palestinian leadership that feels betrayed by the Obama administration, but also by an Israeli government that believes Washington is giving it short shrift.

The reasons for the Israeli rebuff of U.S. overtures reflect the domestic political considerations of Israel Prime Minister Benjamin Netanyahu and those of Obama, as well as America’s fading clout in the Middle East.

Netanyahu is more afraid of a right-wing challenge at home than he is of an angry Obama, who is deeply unpopular in Israel and is losing support among American Jewish voters who have been a Democratic bedrock in the past. The two leaders — an odd couple in political outlook and temperament — have had a chilly relationship for most of Obama’s tenure.

In addition, from the Israeli government’s perspective, the United States is a less useful ally in the new Middle East that is emerging, analysts say, despite the billions of dollars in aid it gives Israel every year.

“Why does the U.S. have less influence with Israel right now? In part because the U.S. has less influence with the Arabs,” said Robert Malley, a special assistant to President Bill Clinton on the Arab-Israeli conflict. He now directs the Middle East program at the International Crisis Group.

U.S. officials privately lament their diminishing clout with Netanyahu’s government, which openly feuded with the White House after Obama, early in his presidency, demanded that Israel cease building Jewish settlements in the West Bank, occupied by Israel in the 1967 Middle East war.

Netanyahu agreed to a temporary freeze at great political risk. But that agreement expired soon after Obama inaugurated a new round of direct Israeli-Palestinian peace talks last year. The negotiations collapsed soon after.

Netanyahu also turned aside an unusually intense U.S. lobbying campaign last month for an Israeli apology for the deaths of nine Turkish civilians last year in a Israeli military raid on an aid flotilla bound for the Gaza Strip, U.S. and Israeli officials acknowledged. One of those killed was also a U.S. citizen.

At issue was Israel’s management of the fallout from the raid on the ship headed to Gaza, which has been under the control of the armed Palestinian movement Hamas since 2007. Turkey has been Israel’s closest Muslim ally for years, and the administration urged Netanyahu to issue the apology to preserve the strategically important relationship. Turkey, a NATO member, is also a key U.S. ally.

In recent weeks, U.S. officials proposed a formula in which Israel would issue a broad apology for the Turkish deaths without yielding on the legitimacy of the Gaza blockade or Israel’s right to enforce it. Israel has said the soldiers acted in self-defense.

At least two senior U.S. officials, including Secretary of State Hillary Rodham Clinton, pressed Netanyahu personally to issue the apology and appeared briefly to have reached a tentative deal, according to U.S. and Middle Eastern diplomats briefed about the exchange.

But Israeli Foreign Minister Avigdor Lieberman, a hard-line nationalist, campaigned publicly against any kind of apology, presenting a threat from Netanyahu’s right that he would not ignore.

“The administration wasn’t blind to the domestic configuration, but it argued to Israel that strategic concerns should trump those considerations,” said David Makovsky, a distinguished fellow at the Washington Institute for Near East Policy. “And a number of leading Israeli security officials shared those sentiments.”

Turkish Prime Minister Recep Tayyip Erdogan, who leads his country’s rising Islamist party, has been a frequent critic of Israeli policy since long before the flotilla raid.

“To be fair to Netanyahu, he feels that the golden era of the 1990s, when Israeli and Turkish cooperation was strong, is not coming back,” Makovsky said. “He believed that Erdogan, for his own domestic political considerations, was adamant on this issue and that an apology was not going to change the overall trajectory of the relationship.”

In the past week, Erdogan denounced Israel in a speech as “the West’s spoiled child,” and warned that Turkish naval vessels could be dispatched into the Mediterranean to protect future aid flotillas and challenge Israeli plans to exploit recently discovered natural gas deposits off its coast.

A senior Turkish official, insisting on anonymity to discuss his country’s internal assessment of the situation, said Erdogan would continue to insist on an Israeli apology.

“We have nothing against Israeli people or the Jews,” the official said. “If they apologize and offer compensation, as any friend would do, things will get better. But they will never be the same.”

Obama, too, is facing political challenges at home that make exerting pressure on Israel dangerous to his reelection prospects. The Republican candidate in a special election for a traditionally Democratic House seat in New York City won this week after a campaign in which he sharply criticized Obama’s treatment of Israel.

Obama has called Israel’s settlement project in the territories “illegitimate.” He has also called for negotiations to be based on the boundaries that existed on the eve of the 1967 war, making clear that land swaps would likely have to be made to account for Israel’s settlements.

At the same time, Obama has stood with Israel on the Palestinian statehood bid at some risk to U.S. diplomacy in the region. The perception of Obama as anti-Israel is not widely held, even among American Jews, who supported him overwhelmingly in the 2008 election. But his standing among the community has slipped.

In May, before he called for talks based on the 1967 borders, Obama had the support of 68 percent of American Jews, according to Gallup. That approval rating has fallen to 55 percent, Gallup reports. Even a small decline in Jewish support could hurt Obama in swing states such as Florida.

Some analysts fear that Netanyahu, who studied at the Massachusetts Institute of Technology, may interpret the results of the recent House special election as further proof that he does not need to heed the Obama administration’s appeals.

But, Makovsky said, “Netanyahu knows enough about the American political map to know that every district is not like this one in New York.”

“While he knows that in 2012 the pressures from Washington will be muted, it does not mean he is immune,” he said.