The summit meeting was also shadowed by concerns about the state of the military campaign against the Islamic State group in Iraq and Syria, which Mr. Obama has said is at too early a stage to say whether the United States and its coalition allies are winning.

Mr. Obama denied reports that he had ordered a formal review of the strategy against the militants in Syria. He said that while the White House was constantly reviewing its tactics in both Syria and Iraq, the basic elements of the strategy remained in place.

Rebuffing a growing chorus of skeptics of his strategy, the president said the United States would never make “common cause” with President Bashar al-Assad of Syria in the campaign against the Islamic State, also known as ISIS or ISIL, because that would alienate the country’s Sunni Muslim population.

“We have communicated to the Syrian regime that when we operate, going after ISIL in their air space, that they would be well advised not to take us on,” Mr. Obama said. “Beyond that, there’s no expectation that we are in some ways going to enter an alliance with Assad. He is not credible in that country.”

At the same time, he said, the United States was not exploring ways to remove Mr. Assad from office — a recognition that the campaign against the Islamic State fighters had given Mr. Assad breathing room. Any lasting political settlement in Syria, he said, would have to involve Iran and Turkey, as well as the Assad government’s primary patron, Russia.

While Mr. Obama continued to rule out the use of American ground troops in the campaign — and said the chairman of the Joint Chiefs of Staff, Gen. Martin E. Dempsey, had not recommended using them, either — he said there were cases in which troops might be necessary. After declining to speculate about those scenarios, he did just that.

“If we discover that ISIL had gotten possession of a nuclear weapon,” Mr. Obama said, “and we had to run an operation to get it out of their hands, then yes, you can anticipate that not only would Chairman Dempsey recommend sending U.S. ground troops to get that weapon out of their hands, but I would order it.”