"I think for President Trump at the U.N., the hope is the third time is the charm," said Jon Alterman, the director of the Middle East program at the Center for Strategic and International Studies.
"The first time President Trump went up to the U.N. in 2017, other leaders were so uncertain of what he would want to do that a lot of them stayed away," Alterman said. "The second UNGA, as you remember, is when the president was laughed at by the General Assembly when he talked about the accomplishments of his administration."
But with his third visit to the gathering, the president's unconventional style and norm-defying approach to U.S. foreign policy -- prioritizing an "America First" vision over multilateral cooperation -- is now well established on the global stage.
The most anticipated meeting on Trump's schedule this week is a planned bilateral meeting with the president of Ukraine. The meeting, scheduled for Wednesday, comes amid questions of a whistleblower's complaint over a phone call the president had with a foreign leader involving Ukraine.
A senior administration official, asked what is on the agenda for the meeting, said the president plans to focus on congratulating President Volodymyr Zelensky on his election victory and to offer praise for his anti-corruption reform efforts.
The president is also slated to meet one-on-one with the leaders of Pakistan, Poland, New Zealand, Singapore, Egypt, South Korea, UK, India, Iraq, Japan and El Salvador.
While the possibility of such a meeting has been floated in recent weeks -- and Trump has expressed openness to the possibility -- Iran has rejected the idea.
"Nothing is ever off the table completely, but I have no intention of meeting with Iran," Trump said Sunday as he left the White House. "But I'm a flexible person. We are meeting with a lot of leaders. We have about 15 meetings set up. But Iran is not one of them."
A senior State Department official told ABC News that during the General Assembly, the Trump administration intends to bring the focus on Iran after blaming it for the massive attack. That includes a social media campaign to "troll" Rouhani and Foreign Minister Mohammad Javad Zarif by "tracking where Zarif and Rouhani are going and ... countering their lies and propaganda that they're spewing," the official said.
But even without direct engagement with Iran, Alterman says this week's gathering provides an opening -- and a test -- for Trump to organize a united front in the wake of an attack on a Saudi oil facility that the U.S. has blamed on Iran.
"The Iranians, it seems to me, have laid a trap. They've challenged a president with unilateral instincts to double down on them and isolate the United States from the world," Alterman said. "Iran is a hard problem, but frankly it's precisely the kind of problem that the United Nations was created to address. The president has an opportunity, especially in his bilateral meetings next week, to begin addressing them.
In addition to the president's bilateral agenda, one of the main events of his three days at the U.N. will be his address the General Assembly on Tuesday morning. The White House has declined to provide a preview of the president's remarks.
That evening, the president and first lady will host a diplomatic reception for visiting world leaders.
Trump will also host a meeting Monday morning that the White House is billing is a global call to protect religious freedom and raise concerns about what a senior administration official said is an increase in the targeting of religious communities and houses of worship over the last decade.
The timing of that meeting has drawn criticism, however, because it overlaps with another meeting on the topic of the environment. A senior administration official declined to comment about the scheduling conflict except to say that the administration is putting the focus on the president's religious freedom meeting.
The president will conclude his visit to the U.N. General Assembly with a press conference Wednesday afternoon.
ABC News' Conor Finnegan and Meridith McGraw contributed to this report.