Boris Johnson says the world is 'united in its disgust for any use of chemical weapons, especially against civilians'.
Moscow warns Washington against carrying out a "military intervention on fabricated pretexts" which "could have the most dire consequences".
The French air force has been active in Syria since 2015 to fight Islamic State, but had not targeted government targets until now.
And every time the U.S. hits a Syrian target, there's always a risk that something goes wrong: A USA warplane is shot down, the U.S. accidentally hits a civilian target, or accidentally kills a Russian or Iranian-backed fighter -prompting one or both of those countries to retaliate against the United States.
U.S. Defense Secretary General James Mattis said air strikes will not take place, unless the Syrian President Beshar al-Assad uses chemical weapons again.
"The combined American, British and French response to these atrocities will integrate all instruments of our national power: military, economic and diplomatic", Trump said. The Syrian government has accused Washington of seeking to use it as a pretext for attacking.
Addressing the American public after ordering the strikes, President Donald Trump said he was compelled to act after witnessing what he described as "the crimes of a monster" in Douma.
At least six loud explosions were heard in Damascus and smoke was seen rising over the city, a Reuters witness said. He says one of the missiles hit the Scientific Research Center in Barzeh near Damascus, damaging a building.
Mrs May said chemical weapons had "all too often" been used in recent times.
North Atlantic Treaty Organisation has issued a strong statement of support for its three allies which launched a military strike against Syria over the suspected chemical attack of last weekend. Former Labour foreign secretary David Miliband, now head of humanitarian relief group the International Rescue Committee, said military action needed to be part of a wider political strategy.
As of Friday evening, the White House had not provided any readout of the "deputies level" national security meeting, but White House deputy press secretary Raj Shah told CNN that the president has also been in constant communication with allies, including the British and French, expected to partner with USA military forces in the event of a strike.
Syrian air defenses shot down 13 missiles fired in the US -led attack on the country on Saturday, Syrian state TV said.More news: Alli: Top teams bring out the best in me
Have Syria and Russian Federation responded?
Syrian state TV said missiles targeting Homs were intercepted and did not cause damage, though CNN has been unable to verify this report.
President Trump said: "The goal of our actions tonight is to establish a strong deterrent against the production, spread, and use of chemical weapons".
"We will not stand by whilst innocent civilians, including women and children, are killed and made to suffer".
At a Pentagon briefing, Dunford said "this wave of airstrikes is over", but defense officials added they are prepared for a sustained campaign until the Syrian regime ceases its alleged use of chemical weapons. Militarily, it is a strike against Syria.
Syria has been fighting a civil war for over seven years.
"This is a very focused strike for one goal to make sure that countries around the world will not use weapons of mass destruction on a regular basis", he said.
It was not immediately clear how the Syrian military responded to the attack.
Syrian President Bashar al-Assad's regime was suspected of orchestrating a chlorine attack against the rebel-held town of Douma, near the capital of Damascus, earlier this month.
An Israeli official told CNN that the strikes enforced the red line drawn by President Trump past year.
The UK, United States and France launched "precision strikes" in Syria overnight.