Though Israeli Prime Minister Benjamin Netanyahu publicly clashed with President Barack Obama on Friday and held firm in his stance Monday night, the Israeli leader still needs American help on a looming test: a proposed United Nations vote on a resolution to recognize Palestinian statehood.

The vote at September’s U.N. General Assembly would be mostly symbolic, and carry little legal weight. But passage—which is expected if the resolution proceeds to a vote—would be a visible show of Israel’s isolation on the international stage.

It could also undercut the dormant Israeli-Palestinian peace process—a focus of Mr. Obama’s foreign policy—by removing the promise of statehood as a motivating force. And it would give the Palestinians more leverage if talks do resume.

Mr. Netanyahu told Mr. Obama, in front of the media in the Oval Office on Friday, that the president’s call for peace talks based on Israel’s borders before it gained new territory in 1967, with negotiated land swaps, was a nonstarter.

The Israeli leader, a day after Mr. Obama set out his position in a major speech on the Mideast, said such a retreat would jeopardize Israel’s ability to defend itself.

Mr. Netanyahu reiterated his position Monday night.

“We can only make peace with the Palestinians if they’re prepared to make peace with a Jewish state,” Mr. Netanyahu told a gathering in Washington of the American Israel Public Affairs Committee, the U.S.’s most powerful pro-Israel lobby. “Israel can not return to the indefensible 1967 lines.”

Mr. Netanyahu will address a joint session of Congress Tuesday in which he said he’ll outline the steps for a final agreement to end the Arab-Israel conflict. But the Israeli prime minister offered little indication that he’d advance any major new outreach to the Palestinians or give ground on the core issues of the dispute—Israel’s borders, the status of Jerusalem or the future of Palestinian refugees.

“I intend to speak the unvarnished truth. Because now, more than ever, we need to speak with clarity,” Mr. Netanyahu said to standing ovations, and a few hecklers. “Events in the region are opening people’s eyes to a simple truth: The problems of the region are not rooted in Israel.”

Leading Democrats and Republicans who also spoke at the conference Monday appeared to side with Mr. Netanyahu in his policy dispute with Mr. Obama. “No one should set premature parameters about borders, buildings or anything else,” said Senate Majority Leader Harry Reid (D., Nev.). “A peace process can happen only when both sides seek peace.”

Mr. Netanyahu’s stance and combative tone have won praise from his hard-line political supporters in Israel, who had been unnerved by a speech this month in which Mr. Netanyahu articulated a more moderate view of a peace settlement. Many in Israel, who see the wave of Arab revolutions empowering new parties hostile to their country, say now isn’t the time for concessions.

Yet as Mr. Obama began a six-day European tour Monday, some critics said Mr. Netanyahu’s aggressive stance could undermine the Obama administration’s efforts to lobby European leaders to vote against Palestinian statehood.

“There is panic in Israeli government political circles about the U.N. resolution in September and the U.N. is an arena where Israel has almost zero influence,” said Yossi Alpher, a former Mossad officer who was an adviser to ex-Prime Minister Ehud Barak. “Netanyahu and his aides have got to be saying to themselves, ‘Can I depend on American support after lecturing the U.S. president in the Oval Office?’ ”

Meanwhile, a prime force behind the West Bank’s economic reforms and the U.N. vote, Palestinian Prime Minister Salam Fayyad, suffered a minor heart attack Monday in Texas. The University of Texas-trained economist, who was on a private visit, was in good condition after a procedure and should leave the hospital within days, hospital officials said.

While the U.S. and European backers of a negotiated settlement support a solution in which separate Israeli and Palestinian states coexist, many European nations are on the fence about whether to support Palestinian statehood at the U.N.

Europe has traditionally been supportive of Israel, which would make a snub of Israel at the U.N. particularly embarrassing. Israeli officials hope that if the Europeans and other Western democracies vote against statehood, the resolution will have less heft, even if it passes. “That way it will be just another piece of U.N. paper,” said a senior Israeli official. Israeli officials, however, say they face an uphill diplomatic struggle and believe that most European countries appear to be leaning toward supporting the resolution.

The friction with the U.S. didn’t help the cause. Senior U.S. officials said Mr. Obama was aware his statement would cause friction with the Israeli leader. The officials said he was tough on Israel—showing a commitment to peace talks and encouraging Israel to show some flexibility—in part to convince hesitant European leaders to oppose the Palestinian push for a U.N. statehood vote. Mr. Obama, in his speech, rejected the statehood plan.

The Palestinian leadership, meanwhile, has given up on negotiations and reconciled with the militant faction Hamas, as it pursues the alternative path of statehood recognition at the U.N. in mid-September, when the General Assembly convenes in New York.

Mr. Netanyahu hopes Mr. Obama will argue against U.N. recognition this week, Israeli leaders say. Mr. Netanyahu moved to soften his tone in the wake of the Friday meeting.

On Sunday, after Mr. Obama reiterated his position on 1967 borders in a speech to the American Israel Public Affairs Committee, Mr. Netanyahu praised the U.S. president. “I appreciate his past and present efforts to achieve” peace, the Israeli leader said. A scheduled speech by the Mr. Netanyahu on Monday night to the pro-Israel lobbying group was seen as another opportunity to recalibrate his public stance.