WASHINGTON — When President Trump travels to New York on Sunday for his second visit to the United Nations, he will face tensions with allies in Europe and Asia — but not necessarily of a predictable sort.
Administration officials contend that Mr. Trump’s well-documented rift with the Europeans over his withdrawal from the Iran nuclear deal has been overblown. But they acknowledge that there is a growing risk of a split with South Korea, an ally with which Mr. Trump has been mostly in sync, over the pace of diplomacy with North Korea.
These crosscurrents will be on display during three days of meetings and speeches at the General Assembly — a ritual that some liken to “diplomatic speed dating,” but which Mr. Trump treated last year as just another venue to talk about his “America First” policy.
Iran and North Korea will be dominant themes for Mr. Trump, both in his speech to the General Assembly on Tuesday and the next day at a meeting of the Security Council, where he will be presiding.
The White House backed off a plan to devote the Security Council session to Iran, responding to protests from European officials, who feared that it would showcase divisions over the nuclear deal, which they continue to honor. Mr. Trump’s aides also worried that it could backfire on him by giving Iran’s leaders a platform to confront him.
Now the meeting will be devoted to countering weapons of mass destruction, a topic that will allow Mr. Trump to emphasize the threat from Iran as well as his negotiations with the North Korean leader, Kim Jong-un.
He will press the council to “better enforce the resolutions it has adopted, which are built on international law pertaining to W.M.D.s, to counter the spread and use of the world’s most dangerous weapons,” according to a draft summary of the meeting plan.
While in New York, Mr. Trump will hold meetings with half a dozen leaders: Emmanuel Macron of France, Theresa May of Britain, Benjamin Netanyahu of Israel, Abdel Fattah el-Sisi of Egypt, Shinzo Abe of Japan and Moon Jae-in of South Korea.
Of those, the session with Mr. Moon could be the most important. He will be fresh from his own latest meeting with Mr. Kim in North Korea. Though Mr. Trump welcomed that meeting — which included a pledge by the North to dismantle facilities that produce fuel for warheads — other American officials have expressed frustration that Mr. Kim has yet to take steps to relinquish the rest of his nuclear arsenal.
Mr. Trump’s aides refer to Mr. Moon’s quest for peace between the North and South as the “sunshine policy,” a phrase popularized by one of Mr. Moon’s liberal predecessors, Kim Dae-jung. It is not meant as a compliment.
A senior official said Mr. Moon’s eagerness for a rapprochement on the Korean Peninsula could outrun Mr. Trump’s demand that Mr. Kim give up his weapons — weakening sanctions against the North and reducing the pressure on Mr. Kim’s government.
For weeks, South Korea’s ambassador to the United States, Cho Yoon-je, has been quietly lobbying lawmakers and journalists in Washington to get the White House to make a major concession to North Korea by agreeing to an end-of-war declaration long sought by Mr. Kim.
Mr. Cho has argued that after North Korea halted its nuclear and ballistic missile tests, the United States needed to make such a gesture to keep the peace process moving forward. In some ways, Mr. Cho has become the top representative here for a government in Pyongyang that has no diplomatic presence in much of the West.
Iran’s president, Hassan Rouhani, plans to attend the General Assembly, but Mr. Trump is not actively seeking a meeting with him, according to a senior administration official. That does not rule out the possibility that the two men could run into each other — a scenario that tantalized United Nations watchers when Mr. Rouhani and President Barack Obama were both in New York in 2013. (They never met, but spoke on the phone.)
The White House hopes to use next week’s meetings to drive home its message that the nuclear deal brokered by Mr. Obama was a failure and that European companies are largely complying with reimposed sanctions that compel them to cut their ties to Iran.
The administration is also trying to project an image of unity on Syria. A senior official said Britain, France and Germany supported Mr. Trump’s threat of a potent military response against the government of Bashar al-Assad if it uses chemical weapons again. Britain and France are actively involved in the planning of such an operation.
But the trans-Atlantic fissures could resurface after Nov. 4, when the most draconian sanctions on Iran’s oil industry and financial system are scheduled to go back into effect. Europe has insisted it will continue to do business with Iran; Trump administration officials insist that anyone who does so will be penalized. For countries that depend on Iranian oil, the United States is trying to line up alternative sources of supply, a senior official said.
Still, the nuclear deal appears to have withstood initial doubts about whether it would survive Mr. Trump’s decision to pull out. While Iran could yet abandon the deal, international nuclear inspectors affirm that Tehran continues to abide by the accord.
While the Europeans are relieved that Mr. Trump tweaked the agenda of the Security Council session to take the spotlight off Iran, they scheduled their own meeting for Monday during which foreign ministers from the other signatories to the deal — Britain, France, Germany, the European Union, Russia, China and Iran — will pledge their fealty to it.
The Trump administration seems to recognize that even if they have avoided an irreparable breach with Europe, Iran will continue to be source of irritation.
“We still have a fascinatingly important relationship with Europe,” Secretary of State Mike Pompeo said on Fox on Wednesday evening, “and I’m confident that that trans-Atlantic relationship will always remain.”