Syrian authorities, in a statement carried by SANA news agency, warned protestors to stay away from demonstrations in the main streets of the capital being called for on Facebook.
"The interior ministry asks citizens not to respond to calls on social networks to take part in demonstrations and gatherings in the principal squares of Damascus, for their own safety," it said.
In the latest bloodletting, one demonstrator was killed and 10 hurt when club-wielding security forces attacked a group of people leaving prayers at the Rifai mosque in the capital's western quarter of Kafar Susseh, the Syrian Observatory for Human Rights said.
Among the wounded was the imam of the mosque, Osama al-Rifai.
The Local Coordination Committees, which groups activists on the ground, confirmed the death, but said 12 people had been injured.
Demonstrations were also reported in the northern Damascus quarter of Roukn Edinne and in Zabadani, 45 kilometres (28 miles) north of the capital, the Observatory said.
Separately, the Observatory said one person was killed and five wounded in Kafar Nabel, in Idlib province of northwest Syria.
On Friday, the last during the Muslim fasting month of Ramadan, security forces killed at least seven people as they fired on protesters rallying in their tens of thousands across Syria and vowing to bring down the regime.
An eighth man died in detention, his family told rights groups.
Spurred by calls posted on the Internet, protesters flooded the streets in the north, centre and south of the country, chanting "Bashar, we don't love you, even if you turn night into day," according to activists.
In the latest call for Assad to pay heed, Iran called on his government to listen to its people.
"The government should answer to the demands of its people, be it Syria, Yemen or other countries," Iranian Foreign Minister Ali Akbar Salehi said in Tehran.
"The people of these nations have legitimate demands and the governments should reply to these demands as soon as possible," the ISNA news agency quoted him as saying.
But Salehi warned about toppling the Syrian regime.
"A vacuum in the Syrian regime would have an unpredictable impact for the region and its neighbours," Salehi said, referring to calls by the United States and European leaders for Assad to step down.
In Cairo, an Arab diplomat said suspension of Syria from the Arab League was "not on the table" of the meeting of foreign ministers.
But in a clear allusion to Syria, Arab League chief Nabil al-Arabi said experience had proved "the security option and recourse to force are pointless against revolutions and uprisings demanding radical change when these demands are legitimate."
"We must react positively to the demands of Arab youth," he said, as "the rapid implementation of reforms" was the way to avoid "foreign intervention."
The organisation has been accused of being soft on Assad, who has pledged reforms but continues trying to quell the uprising.
The Wall Street Journal reported the United States and Israel are monitoring Syria's suspected weapons of mass destruction, fearing chemical agents and long-range missiles could fall into terrorist hands.
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