Syrian security forces deployed heavily on the Mediterranean coast on Saturday, after clashes erupted between the new authorities and remnants of the ousted regime.
The official SANA news agency reported that security forces had deployed to Latakia, as well as Jableh and Baniyas farther south, to restore order.
Defense ministry spokesman Hassan Abdul Ghani said the security forces had "reimposed control" over areas that had seen attacks by Assad loyalists.
"It is strictly forbidden to approach any home or attack anyone inside their homes," he added in a video posted by SANA.
The Syrian Observatory for Human Rights said there had been a "relative return to calm" in the region on Saturday, as the security forces deployed reinforcements.
A defense ministry source told SANA that troops had blocked roads leading to the coast to prevent "violations".
Latakia province security director Mustafa Kneifati said: "We will not allow for sedition or the targeting of any component of the Syrian people.
"We will not tolerate any acts of revenge under any circumstances," he told SANA.
The Alawite heartland has been gripped by fear of reprisals for the Assad family's brutal rule, which included widespread torture and disappearances.
The United Nations envoy for Syria, Geir Pedersen, decried "very troubling reports of civilian casualties".
He called on all sides to refrain from actions which could "destabilize Syria, and jeopardize a credible and inclusive political transition".
The International Committee of the Red Cross urged all parties to "ensure unimpeded access to health care and protection of medical facilities".
"First responders and humanitarian workers must be allowed safe access to provide medical aid and to transport the wounded and dead," it said in a post on X.
Lebanese legislator Haidar Nasser, who holds one of the two seats allocated to the Alawite sect in parliament, said that people were fleeing from Syria for safety in Lebanon. He said he didn't have exact numbers.
Nasser said that many people were sheltering at the Russian air base in Hmeimim, Syria.