UNITED NATIONS—French President Emmanuel Macron delivered an emphatic defense of multilateral diplomacy at the United Nations General Assembly on Tuesday, disagreeing with earlier comments by U.S. President Donald Trump that nations should put their own interests first.

“We have allowed the idea to proliferate that multilateralism is a kind of game, a game for diplomats sitting around a table,” Mr. Macron said. “”Today, more than ever before, we need multilateralism” to address global issues ranging from war to climate change.

In his speech, Mr. Macron openly disagreed with Mr. Trump on three key policy issues: the North Korea crisis, the 2015 Iran nuclear deal and climate change.

On North Korea, Mr. Macron said Pyongyang’s nuclear and ballistic missile provocations are an existential threat to the world but that France’s responsibility is to work with China and Russia to resolve the crisis politically and bring North Korea to the negotiating table.

“France rejects escalation and will not close any door to dialogue,” Mr. Macron said. Mr. Trump took a more aggressive posture in his speech earlier, saying the U.S. would “totally destroy” North Korea if forced to defend itself or its allies.

Mr. Macron also called on the U.S. not to abandon the Iran nuclear deal and said at a news conference after his speech that he had told Mr. Trump in private a day earlier that the deal was working and that Washington should remain committed.

“I don’t understand what the substitute plan is. If we simply throw away this agreement, we can’t replace it,” Mr. Macron told reporters. He said he doesn’t want to find himself in a “no man’s land” where Iran is free to develop nuclear weapons with no international monitoring if the deal were canceled.

Mr. Macron’s position on Iran falls in line with what’s been said by four other world powers that are signatories to the deal. The U.K, Germany, China and Russia all said they want to stick with the agreement.

Mr. Macron said he advocates an approach that would preserve the Iran deal but pressure Iran with sanctions to curb its ballistic missile program and its policies in the Middle East.

The Paris agreement on climate change marked another area of disagreement between Paris and Washington. Mr. Trump did not discuss climate change in his U.N. address, although he mentioned the suffering of American people from recent hurricanes in Texas and Florida, events that some scientists believe are becoming more severe.

Mr. Macron, in contrast, said the “planet will not negotiate with us.” He said he fully respects the decision of the U.S. regarding its withdrawal from the Paris Agreement but said the door would be open to a U.S. reversal and that France would work with all governments to implement the accord.

In their prospective speeches, Messers Trump and Macron highlighted competing themes that have emerged from this year’s gathering of world leaders: multilateralism versus nationalism, or engagement versus sovereignty.

Analysts said Mr. Trump’s speech, and the approach he outlined, left an opening for Mr. Macron to fill.

Mr. Trump’s speech “seemed strangely short on calls for partnership, which has been a U.S. strategy at the U.N. since its founding,” said Jon Alterman, vice president at the Center for Strategic and International Studies. “While the president didn’t attack the institution [of the U.N.], he also didn’t make much pretense of trying to lead the member states.”

Mr. Marcon said at his news conference that Mr. Trump “has his position, but we have disagreements. We each have our own beliefs and positions. History will judge us on Iran and on North Korea and on climate.”