Syria's main backer, Russia, which has insisted there was no chemical weapons attack in Douma and accused the West of fabricating evidence of it, was not informed of the strikes in advance, according to the US.
Iran is a key ally of Syrian President Bashar Assad and has sent troops to bolster his forces.
The French defense minister, Florence Parly, said the jets flew from bases in France.
Col. Gen. Sergei Rudskoi of the Russian military's General Staff says Saturday's strike hasn't caused any casualties and Syrian military facilities targeted by the U.S., Britain and France have suffered only minor damage.
A child cries following an alleged chemical weapons attack, in what is said to be Douma, Syria, in this still image from video obtained by Reuters, April 8, 2018.
"We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents", he added. Russian Foreign Ministry spokeswoman Maria Zakharova said the U.S. strikes had hit the Syrian capital when the country "finally" had a chance at peace. "But politically, it is a strike against Russian Federation", he said. Assad and Russian Federation have denied roles in the attack. Again, the idea was to show Assad that the USA would not tolerate such actions and thus deter him from ever doing so again.
Russia's ambassador to the United States said there would be consequences for the military strikes, adding that it was not acceptable to insult Russia's president.
"But should the United States and our allies decide to act in Syria, it will be in defense of a principle on which we all agree". "This time, our allies and we have struck harder".
"I think it is right that the global community has come together and said we will not accept this", she added.
Mrs May said chemical weapons had "all too often" been used in recent times.
Theresa May declined to say whether Syrian President Bashar al-Assad should stay in power and said talks with allies would continue on finding a political solution to the civil war.
He said that the goal of the action was "to establish a strong deterrent against the production, spread, and use of chemical weapons".
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"This collective action sends a clear message that the worldwide community will not stand by and tolerate the use of chemical weapons", Mrs May told a press conference.
A second witness said the Barzah district of Damascus had been hit in the strikes.
"Britain's defense ministry said "very careful scientific analysis" had been applied to maximize the destruction of stockpiled chemicals while minimizing any risk of contamination to surrounding areas".
Trump chastised Syria's two main allies, Russia and Iran, for their roles in supporting "murderous dictators", and noted that Russian President Vladimir Putin had guaranteed a 2013 worldwide agreement for Assad to get rid of all of his chemical weapons.
The strikes this morning targeted three sites associated with the Syrian government's chemical weapons programme.
The Russian defence ministry said none of the rockets launched had entered zones where Russian air defense systems are protecting facilities in Tartus and Hmeimim.
Experts from the worldwide chemical weapons watchdog, the Organization for the Prohibition of Chemical Weapons, were en route to the alleged chemical weapons attack site in Douma before the joint military strike was launched.
The army said almost 110 missiles hit targets in the capital Damascus and other territory, and air defence systems brought a lot of them down.
A US defense official said the US Air Force used B-1B bombers in the Syria strike.
Britain and France have joined the USA in the military operation, Trump said.
Referring to last week's chemical weapon attack he said: "These are not the actions of a man, they are the crimes of a monster instead".
Mattis, who USA officials said had earlier warned in internal debates that too large an attack would risk a confrontation with Russian Federation, described the strikes as a one-off to dissuade Assad from "doing this again".