The White House press secretary, Sarah Huckabee Sanders, said in a brief statement after Trump met with Mattis and other members of his National Security Council: "No final decision has been made".
May told her senior ministers on Thursday that the attack in Douma showed a "deeply concerning" erosion of worldwide legal norms barring the use of chemical weapons.
"But should the United States and our allies decide to act in Syria, it will be in defense of a principle on which we all agree".
"We're having a number of meetings today, we'll see what happens, we're obviously looking at that very closely", he told lawmakers and governors in the Cabinet Room.
Later, he told reporters a decision will "be made fairly soon".
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America is moving naval assets towards the Mediterranean and has already deployed them within missile range of Syria.
May has said that Russia's veto at the Security Council of a vote to create a new inquiry on chemical attacks meant the United Nations could have no role in investigations.
Earlier on Thursday, the Russian ambassador to the UN, Vassily Nebenzia, said that he believes any strike against Syria would violate the UN charter.
Asked if he was referring to war between the U.S. and Russian Federation, he said: "We can not exclude any possibilities unfortunately".
United States officials have refused to rule out direct military engagement with Russian Federation, with the White House saying "all options are on the table". She told her senior ministers on Thursday the Douma events showed a "deeply concerning" erosion of worldwide legal norms barring the use of chemical weapons.
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They nicknamed him "Tiantian" (or "little sweet"), for the joy he brought after years of bitter legal battles and crushing loss. Other babies have their fathers and mothers, but he doesn't. "We will definitely tell him in the future - how can we not?"
The UN Security Council, tasked with maintaining global peace and security, has been riven, with Moscow virulently denying the Douma attack took place, or postulating that it was carried out by rebels. That meant airstrikes, possibly in tandem with France and other allies that have expressed outrage at the alleged Syrian chemical attack, could be launched within hours of a presidential decision.
In Paris, France's Emmanuel Macron upped the pressure on Moscow by stating he had "proof" that the Assad's regime had used chemical weapons, and vowing a response "at a time of our choosing".
Following an emergency Cabinet meeting, Downing Street said ministers had agreed it was "highly likely" Assad was responsible for the attack on Saturday on the rebel-held town of Douma which reportedly left dozens dead.
Formally, the prime minister has the right to go to war without approval from parliament, but a convention has been established in previous conflicts where MPs have a vote either before or shortly after military action begins. U.S. lawmakers questioned whether Trump has the legal authority to order strikes without Congressional approval and opposition parties voiced concern.
But the pinpoint strike did not deter Assad and United States officials, speaking on condition of anonymity, have since investigated as many as 10 suspected chemical attacks. British officials said up to 75 people were killed.
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The Assad regime is known to have stocks of the nerve agent sarin, and has previously used a mixture of chlorine and sarin in attacks, say US officials.