"We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents", he said.
Syrian state television said government forces had shot down more than a dozen missiles, and claimed only the research facility in Damascus had been damaged.
As pictures of the bombing raids aftermath continue to emerge, Mr Trump said he "could not have had a better result".
"This massacre was a significant escalation in a pattern of chemical weapons use by that very bad regime", he added. "Let these united actions send a clear message to the regime - the use of chemical weapons is categorically unacceptable and you will be held to account".
"The attack took place after the colonial forces supporting terrorists realized they have lost control got the feeling that they have lost credibility in front of their people and the world", Assad said.
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He reaffirmed Russia's view that a purported chemical attack in the Syrian town of Douma that prompted the strike was a fake.
"In a powerful show of allied unity, we deployed 105 weapons against three targets that will significantly impact the Syrian regime's ability to develop, deploy and use chemical weapons in the future", Gen.
Syrian state media reported only three people injured, while Russia's Defense Ministry said there were "no victims" among Syrian civilians and military personnel.
Russia's ambassador to the United States responded by saying the attack on its ally "will not be left without consequences".
The Kremlin has repeatedly dismissed the allegations against Syria and said its own experts found no "trace of chlorine or any other chemical substance used against civilians".
Trump said the operation would be conducted in cooperation with the militaries of France and Britain. The targets, according to the General, are a scientific research facility in Damascus, a chemical weapons storage facility west of Homs and a chemical weapons equipment storage and an important command post, also near Homs. He called on Moscow to change course and join the US and its allies in seeking a more responsible regime in Syria.
Trump told the nation in his address the United States "cannot purge the world of evil or act everywhere there is tyranny".
"We have sought to use every possible diplomatic channel to achieve this", the prime minister said.