Washington also cautioned Syrian President Bashar al-Assad against broadening the conflict.
"As a guarantor of this de-escalation area with Russia and Jordan, the United States will take firm and appropriate measures in response to Assad regime violations," State Department spokeswoman Heather Nauert said in a statement late on Friday.
A war monitor, the Britain-based Syrian Observatory for Human Rights, reported on Wednesday that Syrian government forces fresh from their victory this week against an ISIS pocket in south Damascus were moving into the southern province of Deraa.
Syrian state-run media have reported that government aircraft have dropped leaflets on terrorist-held areas in Deraa urging fighters to disarm.
The US warning comes weeks after a similar attack on a de-escalation zone in northeastern Syria held by US-backed Syrian Democratic Forces. US ground and air forces repelled the more than four-hour attack, killing perhaps as many as 300 pro-Assad militia members, many of them Russian mercenaries.
They have recaptured all remaining insurgent areas near Damascus in recent weeks, including the densely populated eastern Ghouta area, as well as big enclaves in central Syria.
The government is now in its strongest position since the early months of the war in 2011, although still a long way from achieving Assad's aim of reasserting sway over all of Syria.
Anti-Assad terrorists still control two large contiguous areas of territory in the northwest and southwest. Kurdish and allied Arab militia backed by the United States hold the quarter of Syria east of the Euphrates.
The government's gains have brought it to a point where any new military campaign risks putting it in conflict with foreign powers.