Last April, the US launched several dozen Tomahawk cruise missiles at a Syrian air base in response to what it called illegal Syrian use of chemical weapons.
Mattis also said on Friday that the US government was concerned about the Syrian government's use of sarin gas, but acknowledged that he did not have evidence to prove that it was using the nerve agent.
Such allegations were timed to undermine the efforts to resolve the Syrian war through a peaceful settlement between the Syrians without foreign interventions, it noted.
The United States is suspicious, Mattis said, because in addition to the reporting on the ground, the Assad government has been caught using chemical weapons against the Syrian people before.
A deadly sarin attack on a rebel-held area in April prompted Trump to order a missile strike previous year on the Shayrat Airbase, from which the Syrian operation is said to have been launched.
"We're even more concerned about the possibility of sarin use", he said.
The attack comes a day after Syria's former al-Qaeda affiliate claimed responsibility for the downing of a Russian warplane as it flew low over Saraqeb in northern Syria, apparently using a surface-to-air missile.
In his remarks Friday, Mattis alluded to the April attack, saying, "So they'd be ill-advised to go back to violating" the global prohibition on the use of chemical weapons.
However, another official said that the Trump administration hopes that stepped-up worldwide sanctions and diplomatic pressure against Damascus will help rein in Syria's chemical weapons program. He stressed that the United States did not have evidence of sarin gas use. Make a donation and help pay for our journalism.