“In a place like Syria, where there’s no ultimate military victory to be won,” Mr. Obama said, “we’re going have to pursue the hard work of diplomacy that aims to stop the violence and deliver aid to those in need and support those who pursue a political settlement and can see those who are not like themselves as worthy of dignity and respect.”

There are a couple of explanations for Mr. Obama’s circumspect tone. The obvious one is that he has only four months left in office, which means that intractable problems like Syria are not going to be fixed on his watch. Mr. Obama also finds himself in a political bind: He does not want to saddle Mrs. Clinton with policies that could backfire with voters, like a new plan to push Israel and the Palestinians back to the bargaining table.

Mr. Obama was reticent even about his diplomatic achievements. The nuclear agreement with Iran, for example, consumed him and Mr. Kerry for months, requiring a titanic battle against opponents on Capitol Hill and months of diplomatic repair work with allies in the Persian Gulf. Yet on Tuesday Mr. Obama described the deal’s benefits in the blandest terms, saying that it “enhances global security and enhances Iran’s ability to work with other nations.” He coupled this unenthusiastic boast with a warning about another major proliferation threat, North Korea, which recently tested another bomb.

Whatever its long-term risks and payoffs, the Iran nuclear deal remains a source of political static in the United States. To the extent that Mrs. Clinton refers to it on the campaign trail, which is not often, she mostly promotes her credentials to police Tehran aggressively.

For his part, Mr. Obama saved his activism for what would otherwise be a less controversial issue: the plight of refugees. He led a meeting of fellow leaders to nail down commitments from countries to take in more displaced people, and to spend more to integrate them. But even here, in an election year in which fears of terrorism loom large, the constraints on Mr. Obama were clear. In noting that the United States had agreed to admit 110,000 refugees in 2017, up from 85,000 this year, he said that “refugees are subject to more vigorous screening than the average tourist.”

Mr. Obama’s annual speeches to the United Nations are a good way to track the evolution of his foreign policy. The soaring ambition of 2009 gave way to a more restrained tone in 2013, when Mr. Obama acknowledged the limits of American military force. A year later, however, the president struck a more hawkish tone, trying to enlist the world in the fight against the Islamic State and promising to resist Mr. Putin’s aggression in Central Europe with sanctions — and force, if necessary.