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No one in the White House, the Israeli government or among Palestinian officials is publicly predicting a breakthrough out of the three-way Mideast meeting that President Barack Obama is hosting here. And yet the session Tuesday is seen as a crucial step for Obama.

After seeing Israeli Prime Minister Benjamin Netanyahu andPalestinian President Mahmoud Abbas separately, Obama is bringing the two together for the first Israeli-Palestinian meeting since Netanyahu took office in March. Taking place on the sidelines of this week’s annual U.N. General Assembly here, just the fact that the meeting is scheduled is big news.

Even if little more than a photo opportunity, it will probably be the most-watched portion of a marathon day of international diplomacy for Obama, a 12-hour sprint through many high-profile global problems and disputes.

In addition to the three-way Mideast talks, Obama meets the Chinese president at a fraught time in the Washington-Beijing relationship; plays luncheon host, as America’s first black president, to sub-Saharan African leaders for talks on boosting opportunities for young people in their poverty-stricken nations; delivers key speeches toformer President Bill Clinton‘s Global Initiative and to a U.N. heads-of-state session on the stalled issue ofclimate change; and ends the day with a U.N.-sponsored leaders dinner.

The Israeli-Palestinian sit-down wasn’t announced until Saturday and comes with the two sides still far apart on what it would take to resume peace talks that broke off in 2008.

U.S. envoy George Mitchell failed last week to bridge the gap between the two sides on the issue of Jewish settlements in Palestinian territory, putting the long hoped-for three-way meeting in doubt. Obama has askedIsrael to freeze all settlement construction, a condition for Abbas to resume negotiations. But Israel has only committed to a partial halt.

Still, the sides decided to go ahead, even though Obama is considered unlikely to resolve the settlement showdown and announce a relaunching of peace talks.

“We have no grand expectations out of one meeting,” White House spokesman Robert Gibbs said.

One reason to have the meeting is the need to get momentum going.

“The U.S. wants to and the U.S. needs to negotiate in public,” said Jon Alterman, a senior fellow in Middle East policy at the Center for Strategic and International Studies and a former State Department official inPresident George W. Bush‘s first term. “There’s a perceived need for the U.S. to visibly be involved in making progress on Arab-Israeli issues.”

Obama opens his day with brief remarks to a climate summit convened by U.N. Secretary-General Ban Ki-moon. As an opener for Wednesday’s main General Assembly meetings, Ban invited all leaders to the climate summit, hoping to generate political momentum for crucial talks in Copenhagen in December on a new global treaty to curb global warming.

Over 100 leaders plan to attend, the largest number ever to discuss climate change.

Susan Rice, the U.S. ambassador to the United Nations, said Obama will “reaffirm the U.S. commitment to addressing the challenge” — something he hasn’t done previously before what she called “the entire global audience.”

Yet Obama appears before fellow leaders with little to show in his own country on the issue so important to him. A source of great disappointment about Obama in Europe, a House bill to limit greenhouse gas emissions was passed in June but has languished in the Senate and probably won’t go anywhere until next year, if at all.

“Clearly, the road is rough ahead,” Rice said. “But I think it is significant that you will have many heads of state … all together and seriously addressing this problem.”

With Chinese President Hu Jintao, Obama has a full plate.

A little more than a week ago, the president penalized China, citing thousands of lost U.S. jobs when slapping punitive tariffs on all Chinese-made tire imports. Though the move appears unlikely to spark a trade war, it infuriated China at a time when Obama wants Beijing‘s help on climate change and nuclear standoffs with Iranand North Korea.

As a veto-holding member of the U.N. Security Council, China’s support is crucial for getting new sanctions against Iran‘s suspected nuclear weapons program. That topic is especially timely given the upcoming Oct. 1 talks between Iran and an international group that includes the U.S. and China.

China also is the world’s third-largest economy, and is participating in the Group of 20 meetings Obama is hosting later this week in Pittsburgh on the economic crisis.