Syrian state media said there had been a "violation of global law". "She has said all the indications" are that President Bashar Assad's forces were responsible, and the use of chemical weapons "cannot go unchallenged".
He added: "To Iran and to Russian Federation I ask - what kind of regime wants to be associated with the mass murder of innocent men, women and children?"
French President Emmanuel Macron said the strikes had been limited so far to Syria's chemical weapons facilities.
In an unusual move, the Prime Minister will gather her most senior ministers in Number 10 to update them on the latest developments in the crisis, despite the fact that Parliament is still in recess.
Mrs May said she would address Parliament on Monday about the strikes.
"We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents", the USA president said in a televised address.
Syrian opposition activists and rescuers said more than 40 people were killed.
"This was not about interfering in a civil war, and it was not about regime change", May said on Saturday.
Opposition Labour leader Jeremy Corbyn had said Britain should press for an independent United Nations -led investigation into the suspected chemical attack in Douma rather than wait for instructions from Trump on how to proceed.
May doesn't have a majority in Parliament, but the Democratic Unionist Party, which is propping up her government, said it backed her actions.
But May said intelligence pointed to the Syrian government being behind the suspected chemical attack on the rebel-held Damascus suburb of Douma last Saturday, and Defence Secretary Gavin Williamson said speed was "essential". "The use of chemical weapons can not go unchallenged". We can not allow the use of chemical weapons to become normalised - within Syria, on the streets of the United Kingdom, or anywhere else in our world.
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It gives the Prime Minister the green light to join the USA and France in planning military strikes in retaliation. The United States responded with 58 missile strikes that destroyed 20% of the Syrian airforce.
When asked if Syria's Assad could remain leader as long as he refrained from further use of chemical weapons, May said: "This was about, as I have said and you have recognized, this was specifically about the use of chemical weapons".
Senior government ministers were summoned back from a spring break to discuss the attack last week in Douma, which has sparked a tense confrontation between Western nations and Syria and its allies, led by Russian Federation.
"Very careful scientific analysis was applied to determine where best to target the Storm Shadows to maximise the destruction of the stockpiled chemicals and to minimise any risks of contamination to the surrounding area", the ministry said.
"The facility which was struck is located some distance from any known concentrations of civilian habitation, reducing yet further any such risk", the MoD said in a statement.
Russia's ambassador to the UK Alexander Yakovenko said The White Helmets, a group of humanitarian volunteers, are supported by the British Government and are "famous for staging fake chemical attacks".
"I think it is absolutely appropriate that the prime minister and the cabinet made this decision", he told Sky News.
May isn't legally required to do that, though it has become conventional since the 2003 invasion of Iraq for lawmakers to be given the chance to vote before British forces are deployed.
At least six loud explosions were heard in Damascus, and smoke was seen rising over the city even while Trump delivered his remarks.
Jeremy Corbyn, leader of the main opposition Labour Party, has questioned the legal basis for Britain's involvement.
"Bombing can not substitute for diplomacy", he said.