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The president also is sure to speak proudly of the diplomatic track now being pursued in Syria, which aims to eliminate Mr. Assad’s chemical weapons without the use of force. It was the threat of military action, Mr. Obama has said repeatedly, that brought Mr. Assad to the table.

The administration remains open to a similar diplomatic path with Iran, especially under new President Hasan Rouhani.

Mr. Rouhani will address the U.N. on Tuesday afternoon; his address will be watched carefully, but the real focus is on whether he meets face-to-face with Mr. Obama.

There are no meetings scheduled between the two men, and the White House is making clear it’s unlikely the two men will bump into each other in a hallway and begin impromptu talks.

“I don’t think that anything would happen by happenstance on a relationship and an issue that is this important,” said Ben Rhodes, the administration’s national security adviser for strategic communications.