The UK, France and the U.S. are pushing for an independent investigation into allegations that Syrian Government forces are using chemical weapons - a day after launching air strikes on the war-torn country.
The No 10 statement issued following the Cabinet meeting said Mrs May had again described the attack on Douma as a "shocking and barbaric act" which represented a further erosion of worldwide law.
The United States, France and Britain today launched a new bid at the United Nations to investigate chemical weapons attacks in Syria, just hours after firing military strikes against Syrian targets.
She said: "This persistent pattern of behaviour must be stopped - not just to protect innocent people in Syria from the horrific deaths and casualties caused by chemical weapons but also because we can not allow the erosion of the global norm that prevents the use of these weapons".
Following the sarin attack in Eastern Damascus back in August 2013, the Syrian Regime committed to dismantle its chemical weapon programme - and Russian Federation promised to ensure that Syria did this, overseen by the Organisation for the Prohibition of Chemical Weapons.
RUSSIA FAILS TO WIN UN BACKING: The UN Security Council on Saturday opened a meeting at Russia´s request to discuss the allied military strikes.
And reliable intelligence indicates that Syrian military officials co-ordinated what appears to be the use of chlorine in Douma on 7 April.
British planes have conducted more than 1,600 strikes in Iraq and Syria.
In a statement Wednesday, UN Secretary-General Antonio Guterres called on the Security Council to reach an agreement on the "continued use of chemical weapons" in Syria and cautioned the situation could quickly spiral out of control if it didn't.
Scottish leader Nicola Sturgeon put it concisely: "the question that the PM has not answered is how this action taken without parliamentary approval will halt [chemical weapons] use or bring long term peace".
Syrian President Bashar al Assad said the strikes will only increase his government's determination to continue what he described as his 'war against terrorism'.
"But right now this is a one-time shot and I believe that it sent a very strong message to dissuade him, to deter him from doing this again".
Polls in recent days have shown public wariness of military intervention in Syria, with Britain still haunted by its participation in the US-led invasion of Iraq.
"China has always spoken against the use of military force in global relations and spoken for the respect of the sovereignty of all the states, their independence and territorial integrity", the spokeswoman said.
Now we wait to see whether the operation has achieved its aim - to stop President Assad using chemical weapons against his own people.
She specifically cited "the pure horror" of a suspected chemical weapons attack in Douma last Saturday, saying: "The fact of this attack should surprise no-one".
Mattis tells reporters he is certain Assad conducted a chemical attack on innocent people.
A further chemical weapons equipment storage site also in the region of Homs.
"Our teams have been working on this all week and we will need to take decisions in due course, when we judge it most useful and effective", Macron told broadcaster TF1.
Merkel has however ruled out joining any possible strikes against Syria.