The big question as the UN gathers: What to make of Trump?

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. “They continue to be reckless,” she said. “And at that point, there’s not a whole lot the Security Council is going to be able to do,” 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.