What happens next, she said, is up to Assad and to his Russian and Iranian allies.
In the worldwide community, Russian Federation and Iran have also called the Western allegations fabrications and an excuse to attack Syria.
Diplomats said it remained unclear when the council would vote on the proposal, and they were ready to allow time for negotiations to bring Russian Federation aboard.
The Prime Minister spent Saturday evening speaking to world leaders to explain why Britain had joined forces with France and the USA and will insist the three nations are "not alone" in believing it was the "right thing to do".
Some other member states are unhappy with a statement issued on behalf of the European Council on Saturday, which appeared to declare the EU's wholehearted support for the operation by the US, France and Britain.
Despite agreeing to the deal, inspectors have found evidence of an ongoing chemical weapons programme in the country, including systematic use of chlorine barrel bombs and sarin.
Theresa May said the United Kingdom government "strongly supports" the mission.
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"We are concerned they may have tampered with it with the intent of thwarting the efforts of the OPCW Fact Finding Mission to conduct an effective investigation".
Haley also said the response by the Trump administration was "cumulative", taking into account not only the recent chemical weapons attack in Douma, but also other, smaller, attacks.
The OPCW team dispatched to Syria to investigate does not have a mandate to assign blame.
Ahmad, a 25-year-old mechanic who had been displaced from Douma, said the Western strikes were nevertheless too little, too late. The U.S. says that is not true.
In a separate interview, Haley told CBS News that new sanctions against Russian Federation, which has forces in Syria supporting the Assad regime, would be announced Monday that would "go directly to any sort of companies that were dealing with equipment related to Assad and chemical weapons use".
A Syrian firefighter is seen inside the destroyed Scientific Research Centre in Damascus, Syria April 14, 2018. It featured crowds waving flags, fireworks and celebratory gunfire.
Shouts of "Allah, Syria, and only Bashar", a reference to Assad, rang out.
Corbyn said May should remember she "is accountable to this Parliament, not to the whims of the USA president".
Stepping up the pressure on Assad, U.S. Ambassador Nikki Haley said sanctions announced today would be aimed at sending a message to Russian Federation, which she said has blocked six attempts by the U.N. Security Council to make it easier to investigate the use of chemical weapons.
Douma was the last rebel holdout in the eastern Ghouta suburbs, the target of a massive government offensive in February and March that killed hundreds of people and displaced tens of thousands. He said the missiles hit the "sweet spot", doing the expected level of damage while minimizing the unintentional release of toxic fumes that could be harmful to nearby civilians.
In Britain, Prime Minister Theresa May told British lawmakers Monday that Syria, supported by Russian Federation, was trying to hide facts about the attack.