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.

The strikes before dawn Saturday in Syria — which came in retaliation for a suspected chemical attack on civilians a week ago — were the second time in just over a year that Mr. Trump had sent missiles crashing into Syrian military targets, adding American firepower to a civil war that is one of the most complex and multisided conflicts in a generation.

Beyond the immediate question of whether the new strikes actually accomplished the stated goal of diminishing Syria’s capacity to make and use chemical agents, the attack posed the risk of drawing the United States more deeply into a conflict in which Russia and Iran have more invested than ever in keeping Mr. Assad in power.

The United States is “locked and loaded” to strike again if Mr. Assad is believed to renew his use of chemical weapons, Nikki R. Haley, the American ambassador to the United Nations, told the Security Council on Saturday at an emergency meeting called by Russia.

“We are confident that we have crippled Syria’s chemical weapons program. We are prepared to sustain this pressure, if the Syrian regime is foolish enough to test our will,” Ms. Haley said.