Syria's Bashar al-Assad regime appears to have heeded a U.S. warning against staging any new chemical weapons attack as no such action has been launched, U.S. Defense Secretary Jim Mattis said on Wednesday.

"It appears that they took the warning seriously," Mattis told reporters flying with him to Brussels for a meeting of NATO defence ministers. "They didn't do it."

Mattis wouldn't say what specifically triggered U.S. concerns that an attack might be imminent. He said President Donald Trump has showed "how seriously we took them."

Trump's approach has been designed to "dissuade" Syria from using chemical weapons, Mattis added.

Syria and its allies, Russia and Iran, have rejected the U.S. allegation and say Assad's forces never previously used chemical weapons. The U.S. so far hasn't provided details to bolster this week's claim of a chemical attack being planned.

The U.N. has ascribed responsibility to Assad's regime for three previous attacks during Syria's six-year civil war. In April, Trump ordered almost 60 cruise missiles to be fired at the Shayrat base after accusing Syria of killing dozens of civilians in a sarin gas attack.

Asked if any chemical weapons activity beyond Shayrat has been seen, Mattis told reporters traveling with him to Brussels: "I think that Assad's chemical program goes far beyond one airfield."

The White House warned Assad on Monday that he and his military would "pay a heavy price" if it conducted a chemical weapons attack and said the United States had reason to believe such preparations at Syria's Shayrat were underway.