The White House said the government was leading Syria down a "dangerous path" and called for "an immediate end to the brutality and violence".
Activists say at least 32 people were killed in fresh clashes on Friday.
The violence came as government forces moved into the town of Jisr al-Shughour, where it said 120 security personnel had earlier been killed.
Hundreds of civilians have fled north into Turkey to escape the assault.
Assad 'unavailable'In a statement, White House spokesman Jay Carney repeated calls for the Syrian security forces to exercise restraint.
Both state media and activists on the ground also reported troops and tanks advancing on Jisr al-Shughour.
Most residents are believed to have abandoned the town.
The government blamed "armed groups" for the deaths of 120 security personnel in Jisr al-Shughour earlier this week, but some reports said the troops were shot after a mutiny.
Syrian TV said troops had reached the outskirts of the town after securing nearby villages, and that they had killed or captured a number of armed men.
Activists said they had blasted the town with tank fire, but the BBC's Jim Muir in neighbouring Lebanon says there is little indication as to how much resistance the troops are facing in an area whose population has largely fled.
Slaughtered like lambs'
There were reports of large demonstrations against President Assad in many parts of Syria after prayers on Friday.
Security forces are reported to have opened fire in some areas - activists said there were deaths in the coastal town of Latakia, in Deraa in the south, and in a suburb of Damascus.
Friday protests have become a regular event since March, but government efforts to quash them have escalated in recent weeks.
Human rights groups say more than 1,300 people have died in the crackdown, mostly unarmed civilians. The government denies this and says about 500 security forces have died.
More than 3,000 Syrians - mostly women and children - have crossed the border into Turkey to escape the violence, many of them from Jisr al-Shughour. An unknown number of people are thought to have fled to other locations within Syria.
"People were not going to sit and be slaughtered like lambs," one refugee in Turkey told Reuters news agency.
Some of those arriving at the temporary camps have serious gunshot injuries - including a Syrian Red Crescent worker who said he was shot in the back as he tried to help the injured in Jisr al-Shughour.
With the unrest showing no sign of abating, the International Committee of the Red Cross (ICRC) has set up a new camp in Turkey capable of housing up to 5,000 people.
Are you in Syria? Have you travelled from Syria to Turkey to flee the situation there? Send us your comments and experiences.