Theresa May says the use of chemical weapons is a “humanitarian catastrophe” that “cannot go unchallenged”.
The prime minister said “all the indications” pointed towards the Syrian regime being behind a “shocking, barbaric act” in the town of Douma.
She did not comment on US president Donald Trump’s tweet warning Russia to “get ready” for missiles being fired at its ally Syria.
Labour leader Jeremy Corbyn warned that bombing could escalate the situation.
Mr Corbyn told the BBC that Parliament “should always be given a say on any military action”.
“We don’t want bombardment which leads to escalation and a hot war between the US and Russia over the skies of Syria,” he added.
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Medical sources say dozens of people were killed, including children, during the alleged toxic bombing of the formerly rebel-held town of Douma, in the Eastern Ghouta region.
Russia has described the reports of the chemical attack as a “provocation” designed to justify Western intervention against the Syrian regime.
Mrs May described the alleged chemical attack as a “shocking, barbaric act” and said she was “appalled but not surprised” at Russia, which vetoed a US-drafted UN resolution proposing a new inquiry to establish who was to blame.
She said investigations were continuing but that “all the indications” were that the Syrian regime of president Bashar al-Assad, which denies mounting a chemical attack, was responsible.
The UK and its allies were looking at ways to “prevent and deter” the use of chemical weapons, she added.
On Tuesday she spoke on the phone with US President Trump and his French counterpart Emmanuel Macron, agreeing their three countries would work together to take action to “uphold the worldwide prohibition on the use of chemical weapons”.
The SNP called for action against the Syria government, including blocking its “purchasing and importing abilities” and sanctions against key people and companies.
The party’s defence spokesman Stewart McDonald said that while the case for action was clear, air strikes “will not provide the long term solutions needed to end the war”.
Analysis by BBC diplomatic correspondent James Landale
So is Britain hesitating before joining the United States and France in launching air strikes against Syrian targets?
Senior figures in Downing Street deny this adamantly. But there are some voices in Whitehall who believe Theresa May might be displaying her usual caution.
They reckon the prime minister is worried by the possible political fallout of taking military action without parliamentary approval. MPs do not return from their Easter break until next Monday.
Some military folk at the Ministry of Defence, in particular, are poised to deploy their resources and are frustrated they are being made to wait.
The fallout from the attack has sparked a war of words on who was responsible and what the response should be.
On Twitter, President Trump responded to a warning from Alexander Zasypkin, Moscow’s ambassador to Lebanon, that missiles would be shot down and their launch sites targeted if they threatened the lives of Russian personnel.
“Russia vows to shoot down any and all missiles fired at Syria,” he wrote.
“Get ready Russia, because they will be coming, nice and new and ‘smart!'”
On Tuesday President Macron said that if military action was taken, it would target “the regime’s chemical capabilities”, and not the forces of its allies, Russia or Iran.
Speaking in Paris, he said he did “not want an escalation” and that a decision would be made in the coming days.
The information that France had showed “chemical weapons were indeed used and that the regime could clearly be held responsible”, Mr Macron added.
On Tuesday the UN Security Council failed to approve moves to set up an inquiry into the alleged attack on Douma.
As permanent members of the council, Russia and the US vetoed each other’s proposals to set up independent investigations.
The US-drafted resolution would have allowed investigators to apportion blame for the suspected attack, while Russia’s version would have left that to the Security Council.
The Organisation for the Prohibition of Chemical Weapons had said earlier that inspectors would travel to the town to investigate.