The United States and its allies tried to walk a fine line with the airstrikes, sending a strong message to President Bashar al-Assad of Syria without provoking a military response from Russia and Iran, Mr. Assad’s two strongest allies.

The operation on Saturday was more powerful than an airstrike ordered by President Trump last year — this time there were three targets, rather than one, employing twice as many weapons. But it was limited to one night, at least for the moment; was specifically aimed at chemical weapons facilities’ and steered clear of Russian soldiers and bases.

“Right now this is a one-time shot, and I believe it has sent a very strong message to dissuade him, to deter him from doing it again,” Defense Secretary Jim Mattis said of Mr. Assad, although Mr. Trump suggested there might be more to come. “We are prepared to sustain this response,” he said, until Syria abandons its use of chemical weapons.