WASHINGTON — Defense Department officials said on Saturday that American-led strikes against Syria had taken out the “heart” of President Bashar al-Assad’s chemical weapons program, but acknowledged that the Syrian government most likely retained some ability to again attack its own people with chemical agents.

Warplanes and ships from the United States, Britain and France launched more than 100 missiles at three chemical weapons storage and research facilities near Damascus and Homs, the officials told reporters, in an operation that President Trump and Pentagon leaders hailed as a success.

“A perfectly executed strike last night,” Mr. Trump wrote on Twitter. “Thank you to France and the United Kingdom for their wisdom and the power of their fine Military. Could not have had a better result. Mission Accomplished!”

The president, in declaring the mission accomplished, invoked a phrase made infamous by President George W. Bush in 2003, when he declared success in an Iraq conflict that would end up continuing for more than eight years before American troops finally withdrew.