At least 10 people were killed on Friday after security forces fired at demonstrators across the country.
At least eight people were killed in Douma, north of Damascus, and another one was shot to death near the southern town of Deraa, according to a witness and human rights activists.
Dozens of Syrians were wounded in the violence, as thousands of people took to the streets to demonstrate against the regime.
However, according to officials, armed groups opened fire on citizens and security forces in Douma and in the city of Homs, the Syrian state news agency reported on Friday, quoting an official source.
The SANA agency said several people were killed and wounded.
"An official source said an armed group took to the rooftops of some buildings in Douma after midday and opened fire on hundreds of citizens gathering in the city and on security forces," it said.
"In the city of Homs, an armed group opened fire on a gathering of citizens in the Bayyada district, which resulted in the death of a girl," SANA added.
Activists said Syrians took to the streets after Friday prayers in the capital Damascus, Banias on the coast, Latakia port and the southern city of Deraa, where the unprecedented protests challenging Assad's 11 years in power began in March.
Witnesses in the Damascus suburb of Douma said the people killed there were among at least 2,000 people who chanted "Freedom. Freedom. One, one, one. The Syrian people are one," when police opened fire to disperse them from Municipality Square.
The official state news agency SANA reported calm across the country, adding there had been peaceful calls for reform and several gatherings supporting "national unity and... stability."
In his first public appearance since the demonstrations began, Assad declined on Wednesday to spell out any reforms, especially the lifting of a 48-year-old emergency law that has been used to stifle opposition and justify arbitrary arrests.
AFP, Reuters and AP contributed to the story