Mattis also added that the United States was prepared to deploy military options - with media reports indicating that the White House is considering both attacks on multiple targets and a prolonged bombing campaign against the government.
"And so working with our allies and partners from North Atlantic Treaty Organisation to Qatar and elsewhere, we are going to address this issue", Mattis said.
Mattis has previously said a military option is possible.
"Russia vows to shoot down any and all missiles fired at Syria".
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His statement followed Mr Trump's warning for Russian Federation to "get ready" because missiles "will be coming". Get ready Russian Federation, because they will be coming, nice and new and 'smart!' You shouldn't be partners with a Gas Killing Animal who kills his people and enjoys it!', he wrote on Twitter.
The defense secretary referred to Trump's April 9 statement on a "powerful" military response to the alleged chemical attack in Douma, blamed by Syrian opposition media outlets on the Syrian government despite a lack of credible evidence.
Syria has denied using chemical weapons throughout the conflict that began in 2011, including the most recent suspected chemical attack Saturday in a rebel-held suburb of Damascus that killed at least 40 people.
Maria Zakharova, a spokeswoman for the Russian foreign ministry, said any military bombardment by the USA could be an attempt to destroy evidence of the gas attack in Douma.
The Syrian military has also been re-positioning some air assets to avoid the fallout from possible missile strikes, U.S. officials said.