The Syrian government itself seemed more accepting, probably because it was glad to see military power brought to bear against forces that have been fighting Mr. Assad and recently killed many of his soldiers. The Syrian Foreign Ministry said the government “backs any international effort that contributes to the fight against terrorists,” whether it is the Islamic State, the Nusra Front “or anyone else.”

Samantha Power, the American ambassador to the United Nations, informed her Syrian counterpart about the strikes ahead of time, but did not seek permission or disclose the timing or targets. “In fact, we warned them to not pose a threat to our aircraft,” said Benjamin J. Rhodes, the president’s deputy national security adviser. Mr. Rhodes said Mr. Obama had issued the order for the strikes on Thursday, a day after visiting the United States Central Command headquarters in Tampa that would carry out the operation.

In his public appearances on Tuesday, Mr. Obama cautioned again that the campaign against the Islamic State, also known as ISIS or ISIL, would take time. He also cited the strike on Khorasan, the first time he has mentioned the group in public. “Once again, it must be clear to anyone who would plot against America and try to do Americans harm that we will not tolerate safe havens for terrorists who threaten our people,” he said at the White House before his departure for New York.

Most officials speaking publicly on Tuesday characterized the Khorasan threat as imminent. Lt. Gen. William C. Mayville Jr., who is in charge of operations for the Pentagon’s Joint Staff, said the terrorist group was nearing “the execution phase of an attack either in Europe or the homeland.”