UNITED NATIONS—World leaders streamed into New York for the annual United Nations General Assembly gathering this week, taking aim at persistent global challenges that include wars in the Middle East, nuclear weapons in North Korea, the world-wide flow of refugees and climate change.
The assembly also convenes as competition grows between two competing world views: national sovereignty and multilateralism.
More than 130 heads of state and government are expected for the General Assembly, with China and Russia represented by their foreign ministers. The gathering poses an annual challenge to thousands of New York law enforcement officers deployed for the event and to commuters and residents trying to travel across the city.
President Trump arrived Sunday in his hometown of New York and hosted a working dinner with Japanese Prime Minister Shinzo Abe.
On Monday, the president hosted an event discussing the global drug crisis. In the opening session on counternarcotics, Mr. Trump warned of the “scourge of drugs” that continues to claim lives around the world and outlined his administration’s efforts to crack down on drug trafficking and abuse.
“In the United States we are taking aggressive action, securing our border, supporting law enforcement, devoting record funding to the opioid crisis and promoting treatment and recovery,” he said.
Later Monday, Mr. Trump planned one-on-one meetings with the presidents of South Korea, Egypt and France.
World leaders will hear from Mr. Trump when he addresses the General Assembly Tuesday morning; he will lead a Security Council meeting Wednesday on nonproliferation, discussing North Korea, Iran and Syria.
In his Tuesday address, Mr. Trump, after withdrawing U.S. support for a variety of international efforts and openly criticizing alliances such as the North Atlantic Treaty Organization, will advance his view of U.S. sovereignty and international cooperation.
Nikki Haley, the U.S. ambassador to the U.N., said last week that Mr. Trump will address the administration’s preference for sovereignty over multilateralism when international agreements don’t serve U.S. interests.
Under Mr. Trump, the U.S. has pulled out of the Iran nuclear agreement, the Paris climate accord, the Trans-Pacific Partnership trade deal and the Global Compact for Migration. Washington also has forced new negotiations over the North American Free Trade Agreement with Canada and Mexico and other trade deals.
The contrast in tone with European officials will become apparent throughout the week. In his U.N. speech on behalf of the European Union, EU Council President Donald Tusk on Thursday is set to “defend the rules-based international order, which has come under fire under President Trump,” an EU official said.
European Commission President Jean-Claude Juncker directed some veiled criticism at the U.S. for its withdrawal from several multilateral agreements.
“We don’t like the unilateral approach some of our U.N. members are promoting. This is the wrong way,” he told reporters at the United Nations on Sunday.
He said that the EU delegation—with several top officials in town for the U.N. General Assembly—is “here to say that the multilateral approach is not dead. It has to be maintained.”
Mr. Juncker, who in July defused tensions with Mr. Trump in a continuing trade dispute between the U.S. and Europe, is due to meet the U.S. president at a gala dinner for world leaders Mr. Trump is hosting in New York Monday evening.
While no dedicated follow-up meeting on trade had been scheduled between the two leaders as of Sunday evening, Mr. Juncker’s top trade official, Cecilia Malmström, is set to meet U.S. Trade Representative Robert Lighthizer on Tuesday to continue trade talks.
U.N. Secretary-General António Guterres will join the Europeans in offering an alternative to Mr. Trump’s view, according to diplomats.
“At a time of fragmentation and polarization, the world needs this assembly to show the value of international cooperation,” Mr. Guterres said at the formal opening ceremony of the General Assembly last week.
The assembly opened Sept. 18 and concludes on Oct. 3. This week marks the peak of diplomacy with speeches from world leaders, high-profile Security Council meetings, bilateral engagements and side events hosted by different countries.
Secretary of State Mike Pompeo will focus on two of the administration’s core foreign policy priorities while in New York. He is scheduled to deliver a keynote address at a Tuesday summit hosted by United Against Nuclear Iran, a group that is critical of the 2015 nuclear accord. John Bolton, Mr. Trump’s national security adviser, also is slated to address the group.
On Thursday, Mr. Pompeo will be chairman of a U.N. Security Council meeting on North Korea.
The stalled Middle East peace process will be the subject of speeches on Thursday, when Palestinian Authority President Mahmoud Abbas and Israeli Prime Minister Benjamin Netanyahu both address the General Assembly.
Mr. Guterres will hold a high-level meeting on climate on Wednesday with the leaders of U.K. and France expected to attend and deliver remarks.
Other prominent meetings this week will include high-level consultations on Syria, Myanmar and Yemen. Ms. Haley planned to attend the meetings on Myanmar.
—Vivian Salama and Courtney McBride contributed to this article.