"She has said all the indications" are that President Bashar Assad's forces were responsible, and the use of chemical weapons "cannot go unchallenged".
But the Cabinet's call for "action" to prevent further use of chemical weapons included no details on the method or timing of such strikes, while leaving open the possibility of other responses.
Over 60 percent of UK nationals believe that a parliamentary vote on whether London should join the United States in its possible military action against Syria should be held, a survey by YouGov pollster showed on Thursday.
Trump is considering his military options in Syria after Saturday's alleged chemical attack against the rebel-held town of Douma.
May and Trump had also "agreed it was vital that the use of chemical weapons did not go unchallenged and on the need to deter the further use of chemical weapons by the Assad regime".
The BBC said May was ready to give the go-ahead for Britain to take part in action led by the USA without seeking prior approval from parliament, and the Financial Times said the cabinet had agreed to this.
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Watson told The Associated Press he assumes the culprit was someone marching with the teachers, since they have been wearing red. Schools will have the final say on whether firearms actually end up in the classroom, the law just makes it an option.
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Opposition Labour Party leader Jeremy Corbyn, a veteran anti-war campaigner, said Britain should press for a U.N. -led investigation rather than follow the lead of the United States.
"No decision as yet, the Cabinet is meeting in full at 15.30 to discuss", he said, speaking at a Wall Street Journal event in London Thursday morning. May isn't legally required to do that, though it is conventional for lawmakers to be given the chance to vote.
Parliament voted down British military action against Assad's government in 2013, in an embarrassment for May's predecessor, David Cameron.
In 2015 lawmakers approved United Kingdom strikes on Islamic State group targets in Syria, but not on government forces. However, Mrs. May can not be certain of winning one and will be cautious after her predecessor David Cameron famously lost a vote on bombing Syria in 2013.
Brexit Secretary David Davis, who voted against military action in 2013, said "we've got to make this judgment on a very careful, very deliberate, very well thought-through basis, knowing exactly. how strong the evidence is".