“Bernie and Hillary agree on a lot of stuff and pretty much disagree across the board with everything the Republicans say,” he said. “I know Hillary better than Bernie because she served in my administration, and she was an outstanding secretary of state.”

He said there were probably places where Mrs. Clinton agreed with him more than Mr. Sanders, and places where Mr. Sanders might be closer to him than Mrs. Clinton, though he hastened to add that he had not studied their positions closely.

“Ultimately, I will probably have an opinion on it,” he conceded.

But Mr. Obama appeared eager to say that none of the Republicans were ready to lead. Without saying so directly, Mr. Obama suggested that Mr. Trump and the other Republicans would wilt under the pressures of the job he has held the last seven years.

He said that a president must “work with leaders around the world in a way that reflects the importance of the office, and gives people confidence that you know the facts and you know their names, and you know where they are on a map and you know something about their history.”

He added that his successor would have “the nuclear codes with them and can order 21-year-olds into a firefight and has to make sure that the banking system doesn’t collapse and is often responsible for not just the United States of America but 20 other countries that are having big problems, are falling apart and are going to be looking for us to do something.”

Mr. Obama also made clear his reluctance to change course in Syria, where he said Russia had blundered into a “quagmire.”