Compared with handling the Salisbury attack, responding to worldwide calls to retaliate against the Assad regime is a far more challenging undertaking for Mrs May, not least because it is the first time she has been asked to involve Britain in military action since taking office.
Britain would work with United States and France to coordinate an global response, the statement said.
Macron said France had proof that the Syrian regime has used chlorine as a weapon, and told French TV channel TF1 that he was in close discussions with Trump.
The Prime Minister summoned her top team to No 10 amid signs she is preparing to join US-led air strikes against Syrian targets after saying "all the indications" were that President Bashar Assad's regime was responsible for an alleged chemical attack on its own people last weekend.
She continued: "The use of chemical weapons can not go unchallenged".
And even the Conservative chair of the House of Commons defence committee (see quote opposite) is admitting that by making things hard for President Bashar al-Assad, we will be helping evil organisations such as al Qaida.
"But parliament must be involved before any military action is agreed".
Britain is now part of a US-led coalition conducting air strikes against jihadists from the Islamic State (IS) group in Iraq and Syria, and has conducted more than 1,700 such attacks.
"Never said when an attack on Syria would take place. Could be very soon or not so soon at all!" he wrote.
"What we don't want is bombardment which leads to escalation and leads to a hot war between Russian Federation and America over the skies of Syria". Russian Federation has provided Assad with strong military backing.
"The chemical weapons attack that took place on Saturday in Douma in Syria was a shocking and barbaric act", May told reporters in the central English city of Birmingham.
Macron and German Chancellor Angela Merkel have also expressed concern about the "erosion" of the worldwide ban on chemical weapons, and have spoke to each other on the matter, according to a German government statement Thursday.
As with all previous suspected chemical attacks throughout the ongoing conflict, the Syrian government has repeatedly denied any involvement in last weekend's alleged chemical attack on the city of Douma, and has vowed to defend itself against any aggression by the U.S. and its allies.
It remains unclear whether May would seek parliamentary support for any United Kingdom involvement in airstrikes. May is not required by law to consult the House of Commons, but by convention, members of Parliament expect to be consulted.
Action against the Syrian regime itself was ruled out in a parliamentary vote in 2013, and many MPs have called for a vote before any action this time.
Moscow has advised the United States against attacking Syria and is calling for an investigation by the OPCW to determine if chemical weapons were indeed used in Douma.
Many MPs have called for Britain to act against Syria, warning that the use of chemical weapons was in breach of worldwide law and could not be allowed to go unpunished.
The World Health Organization estimated Wednesday about 500 people could have been affected by the suspected chemical attack in Douma, citing reports from its health partners on the ground.