One of Mr. Trump’s primary tasks will be to define how his America First approach — which has led him to pull out of international agreements on free trade and climate change — fits into the world-first mission of the United Nations.
His challenge is “to describe the Trump Doctrine on U.S. global leadership and engagement,” said Zalmay Khalilzad, ambassador to the United Nations under President George W. Bush. “The perception in many parts of the world, including the U.N., is that President Trump is unilateralist and isolationist. Trump has the opportunity to present and describe his vision and strategy. The world will be all ears.”
Mr. Trump arrives in New York at a time of crackling tension over North Korea’s provocative actions and deep uncertainty about what he will do with President Barack Obama’s nuclear agreement with Iran. While foreign leaders once feared that an erratic American presidency was taking shape, they have been reassured, to some extent, that Mr. Trump is settling into a somewhat more conventional foreign policy than many had anticipated, analysts said.
The president has not launched an all-out trade war with China, ripped up the Iran deal or the North American Free Trade Agreement, or moved the American Embassy in Israel to Jerusalem, at least not yet. He has belatedly reaffirmed support for NATO and agreed to send more troops to Afghanistan.
“But America’s friends still see dysfunctionality at the heart of the Trump administration, as key advisers come and go through the revolving door,” said Peter Westmacott, a former British ambassador to Washington. “They remain disheartened by Trump’s announcements on climate change and trade policy.” And “they fear that the fighting talk of this impulsive president could make things worse rather than better on the Korean Peninsula.”
Previewing the week, Lt. Gen. H. R. McMaster, the president’s national security adviser, said Mr. Trump would stress “sovereignty and accountability.” Sovereignty is a term that appeals to American conservatives skeptical about the United Nations. It is also a term, however, used by autocrats like Presidents Bashar al-Assad of Syria and Nicolás Maduro of Venezuela to reject interference by outside powers as they crush opposition.
Mr. Trump will emphasize longstanding efforts to reform what many Republicans see as the sclerotic and inefficient United Nations organization, but aides would not say whether he would commit to the traditional level of American financing as Washington remains in arrears. “You’ll have to wait and see,” said Nikki R. Haley, the ambassador to the United Nations.
Mr. Trump’s advisers made little mention of United Nations priorities like the so-called Global Goals set in 2015 to eliminate poverty and hunger, improve health and the environment, and reduce inequality and gender discrimination by 2030.
“The train has left the station, and he wants the train to come back to the station,” said Sarah E. Mendelson, an ambassador to the United Nations Economic and Social Council under Mr. Obama. “It’s going to go on regardless of what the president does or doesn’t say.”
Mr. Trump will begin the week on Monday with a meeting on United Nations reform. He will meet with the leaders of France and Israel and host a dinner with Latin American leaders. On Tuesday, he will deliver his centerpiece speech to the General Assembly, have lunch with António Guterres, the United Nations secretary general, and meet with Miroslav Lajcak, the president of the General Assembly. He will also meet with the emir of Qatar and host a diplomatic reception.
On Wednesday, Mr. Trump will meet individually with the leaders of Britain, Jordan, Egypt and the Palestinian Authority and host a luncheon with African leaders. On Thursday, he will meet with the leaders of Turkey, Afghanistan and Ukraine and host a lunch with the leaders of South Korea and Japan.
Ms. Haley said Mr. Trump would use his speech to lay down markers. “I personally think he slaps the right people, he hugs the right people, and he comes out with the U.S. being very strong in the end,” she said.
North Korea will be “front and center,” Ms. Haley said, just days after the Security Council escalated sanctions in response to its latest nuclear and missile tests. “And at that point, there’s not a whole lot the Security Council is going to be able to do,” she said, and so “I have no problem kicking it to General Mattis, because I think he has plenty of options,” she added, referring to Defense Secretary Jim Mattis.
The lunch with Prime Minister Shinzo Abe of Japan and President Moon Jae-in of South Korea could help determine the next steps. “They will also be looking to see if Trump is looking towards a long path with North Korea and looking towards diplomacy eventually,” said Lisa Collins, a Korea scholar at the Center for Strategic and International Studies.
The president’s schedule offers various subplots. While Mr. Obama used his first United Nations visit to bring together Prime Minister Benjamin Netanyahu of Israel and Mahmoud Abbas, the president of the Palestinian Authority, Mr. Trump will meet with them separately on different days, and aides played down expectations of progress in his peacemaking initiative. Indeed, aides said the meeting with Mr. Netanyahu would probably focus more on Iran, with the Israeli leader pressing Mr. Trump to revise or scrap the nuclear agreement.
Mr. Trump will not meet with Shahid Khaqan Abbasi, the new prime minister of Pakistan, after recently increasing pressure on the American ally to crack down on Taliban elements operating out of its territory. Instead, Vice President Mike Pence will take that meeting. Likewise, Mr. Trump is not scheduled to attend a meeting on climate change.
Many will watch Secretary of State Rex W. Tillerson, who has been overshadowed by Ms. Haley, to see if he has influence or is on the way out. Mr. Tillerson is scheduled to meet with leaders or foreign ministers from Iraq, India, Russia and Myanmar, among others.
But to the extent world leaders evaluate the new president, Ms. Haley said they should be impressed. “They’re going to find out we are going to be solid, we’re going to be strong,” she said. “No one is going to grip and grin. The United States is going to work.”