(CNN) -- Fights over the economy and health care may be dominating the headlines at home, but President Obama is turning his sights abroad this week.
President Obama will tackle top foreign policy issues, including the global economic crisis, this week.
Starting Tuesday, the president is set to tackle a range of thorny international problems with his counterparts at the United Nations, including nuclear non-proliferation, climate change, the Arab-Israeli conflict and the escalating U.S. war in Afghanistan.
On Thursday, he'll be at a Group of 20 summit in Pittsburgh, Pennsylvania, where he will host a two-day meeting of representatives of the world's largest economies. Issues of financial regulation and executive pay are expected to top the agenda as leaders wrestle with the question of how best to reverse the global economic slide.
The meetings come as Obama retains immense personal popularity overseas but is receiving little backing for controversial decisions such as the deployment of additional military forces to battle al Qaeda and Taliban militants. Watch more on Obama's week ahead »
Several European allies also are worried that Obama may not have the political muscle to carry through with new U.S. pledges of cooperation on global warming and other concerns.
"Our agenda is ambitious," Secretary of State Hillary Clinton said at the Brookings Institution last week when discussing the highly anticipated U.N. session. It stems from Obama's belief that the United Nations is "a critical, central institution," she said.
The United Nations "does not have to be just a diplomatic talk shop," she said. "At its best, it can be an institution that brings the world's nations together to solve global problems."
The U.N. gathering marks Obama's first presidential appearance before the world body. Among other things, he is scheduled to attend a meeting on climate control Tuesday, address the General Assembly on Wednesday and chair a special session of the U.N. Security Council dealing with nuclear non-proliferation Thursday.
Obama will be the first U.S. president to head a meeting of the council. His high-profile U.N. engagement marks a sharp shift in emphasis from George W. Bush's administration, which generally placed a lower priority on the need to act through international institutions.
"A top priority for this administration is to ... actually listen to what other countries have to say," said Peter Yeo, head of the Better World Campaign, which encourages closer cooperation between the United States and the United Nations.
The Obama administration is "less about threats and more about negotiations and diplomacy," he added.
Middle East peace will top the agenda for much of Tuesday as Obama huddles with Palestinian Authority President Mahmoud Abbas and Israeli Prime Minister Benjamin Netanyahu.
The president is hoping to build on the peace process but has "no grand expectations out of one meeting," White House Press Secretary Robert Gibbs said Monday.
The meetings come as hopes for renewed Israeli-Palestinian talks have dimmed despite the diplomatic efforts of George Mitchell, the U.S. envoy for the Middle East.
The United States and Israel have publicly disagreed on Israeli plans to build more housing on land the Palestinians regard as theirs, and U.S. demands for a complete freeze have been ignored by the Netanyahu government.
Abbas has rejected resuming talks with Israel until the Jewish state halts all settlement building in the occupied West Bank and in predominantly Palestinian East Jerusalem.
Obama will also sit down at the United Nations General Assembly's annual session with Japanese Prime Minister Yukio Hatoyama, Chinese leader Hu Jintao and Russian President Dmitry Medvedev.
American officials have been trying to gain Chinese and Russian support for potential new sanctions against Iran in response to Tehran's continued nuclear ambitions. U.S. officials denied last week that Obama's decision to scrap a proposed missile defense system based in Eastern Europe was motivated by a desire to curry favor with Moscow.
Russian officials strongly opposed the system, which many analysts believed posed a potential threat to Russia's strategic nuclear deterrent.
Clinton said last week that Iran's failure to prove that its nuclear program will not be used for military purposes remains a source of "deep concern" to the international community.
She promised continuing "costs" for Iran in the form of diplomatic isolation and economic sanctions if Tehran does not allow greater international oversight of the program.
At the same time, Clinton defended the U.S. administration's decision to open the door to talks with the Iranian government, which has been criticized for cracking down on domestic political opponents in the wake of its disputed June presidential election.
"Dialogue alone doesn't guarantee any outcome," she conceded. But she added that Bush's refusal to engage with Tehran didn't yield any progress on the nuclear issue or reduce Iranian support for terrorist groups.
At the same time, she warned, the Obama White House is not seeking greater diplomatic engagement "just for the sake of talking." She stressed that U.S. officials are hoping for "some movement" on Iran's part by the end of the year.
American U.N. Ambassador Susan Rice said Friday that she doesn't expect a direct meeting between Obama and Iranian President Mahmoud Ahmadinejad at the United Nations session.
Also high on the agenda is Afghanistan.
Top U.S. Gen. Stanley McChrystal has warned Obama that more troops are needed within the coming year, or the nearly 8-year-old war "will likely result in failure," according to a copy of a 66-page document obtained by The Washington Post. He has also called for increased emphasis on protecting civilians and training Afghan troops.
Afghan President Hamid Karzai told CNN on Monday that he backs McChrystal's recommendations. European allies, however, have resisted calls for more assistance.
Some critics of increased military operations have also questioned the legitimacy of Karzai's government in the wake of Afghanistan's contested August presidential election.
Results of the recently completed count gave Karzai 54 percent of the vote, but the numbers won't be certified until authorities investigate allegations of irregularities.
Karzai needs to get more than 50 percent of the vote to avoid a runoff in his bid for a second term. His chief rival, former Foreign Minister Abdullah Abdullah, said he has "no doubt" that Karzai and his supporters worked to rig the vote in the incumbent's favor.
The United States has about 62,000 troops in Afghanistan, with NATO and other allies contributing about 35,000 more. The Pentagon is planning to add 6,000 troops by year's end.
CNN's Alan Silverleib contributed to this report.