The need for the Pentagon to educate civilians in the Trump administration also featured in the decision by Gen. Joseph F. Dunford Jr., chairman of the Joint Chiefs of Staff, to take Mr. Trump’s son-in-law and senior adviser, Jared Kushner, to Baghdad this week to meet with Iraqi authorities and American military officials in Iraq.

Pentagon officials said Mr. Assad’s decision to drop chemical weapons on Idlib most likely included anxiety over the Syrian government’s losses of military gains made in the past two years. But several officials said the remarks by Ms. Haley, Mr. Tillerson and Mr. Spicer could have emboldened Mr. Assad into believing that there would be no retaliation.

At the very least, the Trump administration has been sending mixed messages to Mr. Assad — and to President Vladimir V. Putin of Russia — on its intentions in Syria. Just days after winning the presidential election in November, Mr. Trump signaled in an interview with The Wall Street Journal that in Syria, he would focus solely on bombing the Islamic State. “My attitude was, you’re fighting Syria, Syria is fighting ISIS, and you have to get rid of ISIS,” Mr. Trump said.

Just days after that, Mr. Assad seemed to take those comments to heart, and publicly called Mr. Trump a potential “natural ally” in the fight against terrorism.

“The Syrians can argue that they felt they were given a green light, with the U.S. sending very inconsistent messages,” said Kathleen Hicks, director of the international security program at the Center for Strategic and International Studies.

Mr. Mattis and other military officials in the Trump administration were quick to urge their national security counterparts to respond forcefully to the chemical weapons attack. Over two days, the Pentagon drew up a list of options for responding that was whittled down to one — launching cruise missiles at the Syrian air base of Al Shayrat. Intelligence officials had determined, with a high degree of confidence, that Syrian fighter jets took off from there in launching the chemical attack on Idlib.

Once he was presented with the cruise missile response, administration officials said Mr. Trump — who said he was appalled by the television images of Syrian children killed or injured in the attack — instantly approved the plan presented by Mr. Mattis and General McMaster.