The targets hit from US ships in the Mediterranean Sea included the air base in the central city of Homs from which the Syrian aircraft staged Tuesday's chemical weapons attack, the US official told Reuters, speaking on condition of anonymity.
Trump said the strike on Syria was in the "vital national security interest" of the United States.
He called on "civilised nations" to join US in "seeking to end the slaughter and bloodshed in Syria".
Syrian state TV said "American aggression targets Syrian military targets with a number of missiles".
The poison gas attack on the rebel-held town of Khan Sheikhoun in Idlib province killed at least 86 people, including 27 children, according to the UK-based Syrian Observatory for Human Rights.
Turkey said samples from victims of Tuesday's attack indicate they were exposed to sarin, a highly toxic nerve agent.
"I think what happened in Syria is a disgrace to humanity and he's there, and I guess he's running things, so something should happen," Trump had told reporters earlier on Thursday.
He was expected to deliver an address to the nation from his Mar-a-Lago estate where he was meeting the Chinese President Xi Jinping.
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