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United Nations (CNN) -- President Barack Obama will lay out the U.S. view of the "seismic change" seen around the world in the past year, particularly in the Arab world, when he speaks to the United Nations on Wednesday, aides said. Obama spent Tuesday in one-on-one talks with a variety of world leaders at U.N. headquarters, including the head of Libya's transitional government, Afghan President Hamid Karzai and Turkish Prime Minister Recep Tayyip Erdogan. And he is scheduled to meet Wednesday evening with Palestinian Authority President Mahmoud Abbas, whose push for the world body to recognize an independent Palestinian state has put the Obama administration in a tight spot diplomatically. In talks with Erdogan, Obama said the Palestinian effort would not advance a "shared goal" of resolving the decades-old Israeli-Palestinian conflict, said Liz Sherwood-Randall, a top National Security Council aide. And Ben Rhodes, the council's strategic communications director, said the U.S. goal was to get Israel and the Palestinians back to direct negotiations. "As we've said repeatedly, what we're focused on is how do we get a basis for direct negotiations that can actually achieve a Palestinian state," Rhodes told reporters Tuesday evening. The Palestinian gambit comes after months of upheaval in the region that has seen longtime Arab strongmen toppled in Tunisia, Egypt and Libya. Sherwood-Randall said Obama and Erdogan also talked about putting more pressure on Syria's government, which has tried for months to forcibly suppress demonstrations there. Rhodes said the sweeping changes across the region will take up much of Obama's address to the General Assembly on Wednesday morning and "speak to the momentum of democratic change in the world." "There's been a seismic change in the past year, and I think the discussions today underscore that," he said. Obama's earlier meetings touched on major headlines of the day, with Obama and Karzai discussing the assassination of former Afghan President Burhanuddin Rabbani, who was considered vital to peace efforts in the country. He urged Erdogan to continue work toward patching up Turkey's strained relations with Israel, a vital U.S. ally in the Middle East, and expressed condolences for the deaths of at least three people in a suspected bombing in Ankara on Tuesday, Sherwood-Randall said. And he led a meeting of an open government partnership with Brazil and other countries dedicated to improving government transparency around the world. Earlier, Obama addressed a meeting of the Libya Contact Group, telling the gathered leaders, including U.N. Secretary-General Ban Ki-moon, that the NATO-led military campaign in Libya that helped oust Moammar Gadhafi from power was an example of modern global cooperative action. "This is how the international community should work in the 21st century -- more nations bearing the responsibility and the costs of meeting global challenges," Obama said. "In fact, this is the very purpose of this United Nations. So every nation represented here today can take pride in the innocent lives we saved and in helping Libyans reclaim their country. It was the right thing to do." Obama sought to reinforce a foreign policy strategy that emphasizes cooperation and shared responsibility after what has been criticized as a "might makes right" posture by the United States in past decades. "The Obama administration has dramatically changed America's course at the United Nations to advance our interests and values and help forge a more secure and prosperous world," declared a White House document released Tuesday. "We have repaired frayed relations with countries around the world. We have ended needless American isolation on a range of issues. And as a consequence, we have gotten strong cooperation on things that matter most to our national security interest. " The document cited "concrete results" at the United Nations that it said advanced "U.S. foreign policy objectives and American security," including: The stiffest U.N. sanctions ever against Iran and North Korea; Efforts to stop the proliferation of nuclear weapons and materials; The Libya intervention and subsequent efforts to aid the political transition there; The peaceful independence of Southern Sudan; and, U.N. assistance in Afghanistan and Iraq. In addition, the White House document said the United States is the largest donor of humanitarian assistance for the Horn of Africa famine, with most of the $600 million provided so far funneled through U.N. agencies. On Israel, it said, the Obama administration has "consistently and forcefully opposed unbalanced and biased actions" in the Security Council, the U.N. General Assembly and throughout the U.N. system. Before Obama spoke to the Libya Contact Group, the nation's new flag was raised, reflecting the leadership change from Gadhafi to the National Transitional Council, prompting a standing ovation in the room. "Libya is a lesson in what the international community can achieve when we stand together as one," Obama told his fellow leaders. "As I said at the beginning of this process, we cannot and should not intervene every time there's an injustice in the world. Yet it's also true that there are times where the world should have and could have summoned the will to prevent the killing of innocents on a horrific scale. And we are forever haunted by the atrocities we did not prevent, and the lives we did not save. But this time was different. This time, we, through the United Nations, found the courage and the collective will to act." Obama also lauded the Arab League for requesting the U.N.-sanctioned intervention in Libya, as well as "Arab states who joined the coalition, as equal partners." He pledged continued U.S. support for the NATO-led military mission and humanitarian assistance, and urged the Libyan people to reject "violent extremism" as they embark on democratic transition. "To the Libyan people, this is your chance," Obama concluded. "And today the world is saying, with one unmistakable voice -- we will stand with you as you seize this moment of promise; as you reach for the freedom, the dignity and the opportunity you deserve."