Mattis did not directly speak to U.S. intelligence about Shayrat Airbase.
The Kremlin is dismissing the White House's warning that the Syrian government is preparing a new chemical attack and that President Bashar Assad and his military "will pay a heavy price" if it goes ahead.
Her remarks come about 12 hours after the White House said it had identified "potential preparations" for another chemical weapons attack by Syria.
The French foreign ministry refused to say Tuesday whether it too had information about possible preparations by the Syrian regime for a chemical attack.
"It appears that they took the warning seriously", Mattis told reporters flying with him to Brussels for a meeting of North Atlantic Treaty Organisation defence ministers.
However, Mattis said Syria's chemical weapons threat was larger than any single location.
Syria was said to have destroyed all of their chemical weapons under an agreement reached by the US, Russia, and the Assad regime in 2013.
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Russian Federation pledged to treat all USA aircraft in Syria west of the Euphrates as legitimate targets and to track them with air defense systems.
In April, Trump ordered nearly 60 cruise missiles to be fired at the Shayrat base after accusing Syria of killing dozens of civilians in a sarin gas attack.
The situation at Shayrat airfield has not changed. If you would like to discuss another topic, look for a relevant article.
The Pentagon chief insists the United States is not taking sides in the Syrian conflict, saying late Monday that USA forces would not fire on targets "unless they are the enemy, unless they are ISIS".
"The goal is at this point not just to send Assad a message, but to send Russian Federation and Iran a message", Haley told a House panel.
Also, a senior Russian lawmaker on Tuesday dismissed the US claim as an "unprecedented provocation".
The U.S. cruise missile strike in April was the first intentional U.S. assault on Assad's government or military. But in April, more than 80 people were killed in a suspected chemical weapons attack in north-western Syria.
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Syria maintained it hadn't used chemical weapons and blamed opposition fighters for stockpiling the chemicals.
The U.S.is providing air support and arms to Kurdish-led Syrian forces who are fighting to drive the Islamic State group from Raqqa, the extremists' self-styled capital.
"We consider unacceptable any such threats to the legitimate government of the Syrian Arab Republic", Peskov said.
When asked how he knew Trump's warning had worked, Mattis said: "They didn't do it", a reference to the fact no chemical strike had occurred since Monday.
The White House said the recent preparations in Syria were similar to actions before the April attack.
White House spokeswoman Sarah Huckabee Sanders flatly denied the White House was freelancing on foreign policy.
On Monday, Trump had dinner with Mattis, Secretary of State Rex Tillerson, National Security Adviser H.R. McMaster and other top officials as he hosted Indian Prime Minister Narendra Modi at the White House.
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