The prime minister has agreed with her US and French counterparts that the international community must respond to an alleged chemical attack in Syria.
In phone calls, Theresa May, Donald Trump and Emmanuel Macron said those responsible should be "held to account".
Mr Macron said any strikes would target Syrian government chemical facilities.
But Russia, which provides military support to Syria, has said there is no evidence of a chemical attack.
Medical sources say dozens of people were killed, including children, during the alleged toxic bombing of formerly rebel-held town of Douma, in the Eastern Ghouta region.
Downing Street said the separate phone calls established the countries would work together to take action to "uphold the worldwide prohibition on the use of chemical weapons".
A spokeswoman said the leaders agreed the reported attacks were "utterly reprehensible" and if confirmed, "represented further evidence of the Assad regime's appalling cruelty against its own people and total disregard for its legal obligations not to use these weapons".
Analysis: Will Parliament vote?
by James Robbins, BBC diplomatic correspondent
The US would like any military response to include European powers, but Theresa May would not be drawn by questions on possible British involvement.
She faces the acute dilemma of whether or not to seek parliamentary approval, which she might not get.
To recall parliament before it returns next week, after the Easter recess, would be a huge step, but taking her own decision carries political risk.
Then there's a question of loyalty among international allies.
After Donald Trump took unprecedented action in answer to her appeals for support by expelling record numbers of Russian diplomats from the US after the Salisbury nerve agent attack, is this her payback time?
And how will it look if France joins possible action against President Assad and Britain does not? Would that be confirmation that Paris is the dominant military capital of post-Brexit Europe?
Earlier, US President Trump cancelled a planned trip to Latin America to focus on the issue. He has pledged a "forceful response".
French President Emmanuel 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 evening, the UN Security Council rejected a draft US resolution, which proposed a new inquiry to establish who was to blame.
Russia vetoed the move and China abstained, meaning the resolution could not be passed.
Foreign Secretary Boris Johnson said the result was "hugely disappointing" and accused Russia of holding Syrian people to "political ransom" by supporting President Assad's regime in the country.
A Russian-drafted resolution expressing support for sending investigators from the global chemical weapons watchdog agency to Douma also failed.
The Organisation for the Prohibition of Chemical Weapons had said earlier that inspectors would travel to the town to investigate.
On Tuesday afternoon Mrs May also chaired a National Security Council meeting to discuss the issue of chemical weapons in Syria.
Last year, President Trump ordered a missile strike in retaliation for a Sarin gas attack against a Syrian town.