Raising the alarm about the chemical threat amid Syria's long civil war, USA officials said the Syrian government and the Islamic State group continue to use such weapons, although the militants' arms are said to be more rudimentary.
Mattis told reporters that chlorine gas was known to have been weaponised in attacks in Syria, but added: "We are even more concerned about the possibility of sarin use".
If the worldwide community does not act quickly to tighten the screws on Mr Assad, Syria's chemical weapons could spread beyond its borders and possibly even "to USA shores", the second official claimed.
While the final statement said that the future of Syria should be decided in elections, it did not say whether Syrian refugees would be allowed to take part.
"We are on the record and you all have seen how we reacted to that, so they would be ill-advised to go back to violating the chemical (weapons) convention", Mattis said.
The claims come amid reports of continued chemical attacks in Syria.
A senior USA official told AFP that military options against Damascus similar to those launched in April 2017 were always on the table and "always feasible".
"Deterrence is something that you have to continually work at", said the second official.
President Donald Trump has not ruled out additional military action to deter attacks or punish Assad, administration officials said, although they did not suggest any action was imminent.
The Assad regime on Thursday attacked a residential suburb of Damascus with chlorine gas, according to the White Helmets, a pro-opposition Syrian civil defense agency.
Syrian President Bashar al-Assad's regime has been linked to multiple chemical weapons attacks, and the USA suspects Russian Federation is enabling it.
Several children were also affected, the group said. "And that use will spread to USA shores".
The US officials also said Islamic State militants have sporadically used chemical weapons, such as sulfur mustard and chlorine, some via improvised explosive devices.
Nauert's comments follow a suspected chlorine gas attack in the rebel-held territory of Eastern Ghouta, on the outskirts of Damascus, on Thursday.
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