UNITED NATIONS — President Trump thrust his commitment to an “America First” foreign policy back onto the United Nations General Assembly on Tuesday. But in his second address on this diplomatic stage, he sounded as eager to claim credit for his achievements after 20 months in office, as he was to disrupt the world order.

If Mr. Trump had changed, so had his audience — no longer as daunted by the insurgent figure who left them slack-jawed last year when he vowed to “crush loser terrorists,” mocked North Korea’s leader as “Rocket Man” and declared that parts of the world “are going to hell.”

This time, emissaries from around the world listened quietly as Mr. Trump fulminated at foes like Iran and failing states like Venezuela. They nodded as he singled out an enemy-turned-partner, Kim Jong-un of North Korea, expressing optimism for a diplomatic opening that would have seemed far-fetched even a year ago.

But when Mr. Trump declared, “In less than two years, my administration has accomplished more than almost any administration in the history of our country,” the crowd broke into murmurs and laughter.