Speaking before the U.N. General Assembly last year, President Obama urged those who support a two-state solution to the long conflict between Israelis and Palestinians to “reach for what’s best within ourselves.”

“If we do,” he said, “when we come back next year, we can have an agreement that will lead to a new member of the United Nations — an independent, sovereign state of Palestine, living in peace with Israel.”

That goal has grown more remote since Obama spoke those words. As he returns Wednesday to address the General Assembly, Obama is facing a vexing diplomatic challenge: to explain how his hopes of last year square with his opposition this year to a Palestinian bid for statehood.

Obama will specifically address, his advisers say, the lack of progress in resolving the Israeli-Palestinian conflict, an issue he made a priority on taking office. Obama will seek to draw a distinction between his support for Palestinian statehood and his opposition to pursuing that goal through the United Nations.

He will be doing so for two audiences — one suspicious of his intentions toward Israel, the other seeking to understand how he can encourage self-rule in some places and not in others. His ability to make his case has implications for his reelection prospects — highlighted Tuesday when a leading GOP rival forcefully criticized his handling of Israel — and for his diplomatic overture to Muslims abroad.

“We would not be here today at the very precipice of such a dangerous move if the Obama policy in the Middle East wasn’t naive, arrogant, misguided and dangerous,” Texas Gov. Rick Perry said in a speech here attended by Israeli and American Jewish leaders.

Until now, administration officials have explained Obama’s opposition in practical terms, arguing that a statehood resolution approved over the objection of Israel will only make it harder to return to direct peace talks over final borders, the status of Palestinian refugees and their descendants, and the future of Jerusalem.

“The point that the president will make is, at the end of the day, peace is going to have to be made between the parties,” said Ben Rhodes, the deputy national security adviser for strategic communications. “There’s no shortcut.”

But the administration’s argument places it firmly outside the prevailing sentiment of the Middle East, swept up in the new freedoms of the Arab Spring.

Last week, Palestinian leader Mahmoud Abbas announced that he will bring a statehood resolution to the Security Council, and administration officials reiterated Tuesday that the United States will veto the measure if needed.

U.S. diplomats are working to round up enough votes against the resolution to make a U.S. veto unnecessary, although it remains unclear whether a majority of the 15-member council will oppose a bid that is backed by most U.N. members.

On Tuesday, Obama met with Turkish Prime Minister Recep Tayyip Erdogan, an outspoken advocate of the Palestinian statehood bid. White House officials said Obama told Erdogan that U.N. recognition would not enhance the prospects for the creation of a Palestinian state.

At lower levels, U.S., European and Middle Eastern officials searched for ways Tuesday to either head off the Palestinian bid or soften its impact.

One diplomatic track was aimed at preventing, or at least delaying, Abbas’s statehood request, a goal seen as increasingly unlikely. Another approach sought to create a formula for restarting Israeli-Palestinian negotiations regardless of what happens with the statehood bid, Western diplomats said.

Abbas appears determined to submit the Palestinian membership application to Secretary General Ban Ki-moon on Friday. But diplomats note that ensuing diplomatic maneuvering within the Security Council could delay a vote on the proposal for days, weeks or longer.

Obama plans to meet separately Wednesday with Israeli Prime Minister Benjamin Netanyahu and Abbas.

Obama’s U.N. address last year came a few weeks after he inaugurated a new round of direct Israeli-Palestinian peace talks, and there was a measure of optimism surrounding his remarks.

Netanyahu had agreed to a temporary freeze of the construction of Jewish settlements in the West Bank.

Shortly after Obama’s address, the settlement moratorium lapsed, and Netanyahu did not renew it. The direct negotiations soon collapsed, and Abbas’s decision to push for U.N. recognition during this General Assembly session gained momentum in the ensuing months.

With his domestic approval rating at a low point, Obama has little political room to maneuver on a polarizing foreign policy issue, particularly for American Jews.

But a plurality of Americans say the United States should recognize Palestine as an independent state, even as public sympathies continue to lie with Israel in the conflict, according to a new poll by The Washington Post and the Pew Research Center.

About a third of all those surveyed expressed no opinion about whether the United States should recognize a Palestinian state, and nearly four in 10 did not offer an assessment of Obama’s policies toward Israel and the Palestinians.

Of those expressing an opinion, 42 percent said they back U.S. recognition of a Palestinian state; 26 percent oppose such a move.

Polling director Jon Cohen and staff writers Philip Rucker and Joby Warrick in Washington contributed to this report.