In his address, President Trump told the nation that the strikes were a direct result of Russia's failure to prevent Assad from using chemical weapons.
There was no immediate word on any casualties or damage.
He added the the US and it's allies are prepared for "sustained" response until Syrian government stops use of chemical weapons.
Mattis also said Thursday that options for Syria will be discussed at a National Security Council meeting Thursday. Earlier this week he had tweeted that USA missile strikes against Syria could happen "very soon or not so soon at all".
US-led coalition forces launched a coordinated attack on Syria in an operation tagetted to end the "criminal" regime of Bashar al-Assad which has been accused of gassing innocents in an alleged chemical attack.
"We have proof that last week ... chemical weapons were used, at least chlorine was, and they were used by the Assad regime", he said.
President Trump warns Assad: "Big price to pay" for fatal Syria attackThe strike came as Trump has alluded to military action in Syria all week, even tweeting on Wednesday that Russian Federation should be "ready" because "nice and new and "smart" missiles "will be coming".
Russian military sources told Kommersant this week that a USA strike on Russia's air base or naval facility in Syria would have catastrophic consequences.
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Haley told an emergency meeting of the U.N. Security Council that should the United States and its allies decide to act in Syria it will be to defend "a bedrock worldwide norm that benefits all nations" - the prohibition on the use of chemical weapons.
Syrian news outlet Al-Masdar News reported cruise missiles struck rural Damascus and caused explosions at Dumayr Airbase.
The last time Syria dropped a chemical weapon on its own people, Trump launched missiles at an airbase that had been abandoned.
Syria and its ally Russian Federation deny such an attack happened.
Top Senate Democrat Chuck Schumer is calling the airstrikes appropriate, but said "the administration has to be careful about not getting us into a greater and more involved war in Syria". But afterward the White House said that "no final decision has been made".
"The nations of the world can be judged by the friends they keep", the president said.
A fact-finding mission from the Organisation for the Prohibition of Chemical Weapons is expected to head to Douma.
"I watched the President's speech tonight, and my thoughts are with the men and women in uniform who are in harm's way", said Sen. A YouGov poll showed just one in five members of the public support a strike on Syria.
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