Protests took place at dawn on Friday in five residential neighbourhoods of the capital in support of the rebel Free Syrian Army (FSA), and to call for President Bashar al-Assad's downfall, the Syrian Observatory for Human Rights said.
Demonstrations were also held in the northern city of Aleppo while activists began gathering in other protest hubs for rallies after the Muslim weekly Friday prayers, as has been customary since an anti-Assad revolt erupted in March 2011.
The Observatory said six civilians were killed on Friday, four of them, including three teenagers, by regime forces' gunfire as they guarded their farm in the village of Chizar, in central Hama province.
The Britain-based Observatory also said that at least 34 people, including 24 civilians, were killed on Thursday, in violence across the country, including the shelling by regime forces of the rebel stronghold of Rastan, in central Syria.
The outgoing leader of Syria's largest opposition group charged on Thursday that the deeply-divided opposition had failed its people.
Burhan Ghalioun, speaking to AFP after the main opposition Syrian National Council accepted his resignation as leader, said the chasm in its ranks between Islamist and secularists had let down the Syrian people and played into Assad's hands.
"We were not up to the sacrifices of the Syrian people. We did not answer the needs of the revolution enough and quickly enough," Ghalioun said.
"I submitted my resignation precisely to say that this path of division between Islamist and secular doesn't work and I think the Syrian regime has won in that respect because since the beginning it has tried to play on this division," the Paris-based academic said.
The FSA, made up largely of dissidents from the regular army, insisted that helping the Syrian people obtain their freedom was among its top priorities, in a statement outlining its goals and principles.
It also said it would refer to international courts those responsible for war crimes against the Syrian people, and pledged total commitment to international standards of human rights.
The rebel group, made up largely of dissidents from the regular army, further promised it would not intervene in the political process after the fall of the Assad regime.
A UN panel said on Thursday government forces were to blame for most abuses in the violence that has raged on daily despite a UN-backed ceasefire supposed to take effect April 12.
The Independent Commission of Inquiry on Syria, also highlighted in a report released in Geneva the killing, capture and torture of army and security force personnel, as well as suspected informers, by anti-government groups and their growing use of homemade bombs.
More than 12,600 people have been killed in Syria since the revolt against Assad's rule broke out in March last year, including nearly 1,500 since the UN-backed truce took effect, according to Observatory figures.
Assad, speaking during talks with a visiting minister from key Middle East ally Iran on Thursday, insisted his government could find a way to end the 14-month uprising against his rule.
"Syria has been able to overcome the pressures and threats it has faced for years and is able to get out of this crisis thanks to the strength of its people and commitment to unity and independence," state media quoted him as saying.
Assad's comments came as parliament convened for the first time since a controversial May 7 election boycotted by the opposition and dismissed by the West as a farce.
Despite changes to the constitution ending the Baath's five decade domination of power, more than 160 of the 250 members of parliament are Baathists and the legislature voted by 225 to eight to elect ruling party member Jihad Lahham as its speaker.
A donors' working group set up by the Friends of Syria organisation formed by Arab and Western governments critical of the Assad regime meanwhile met in Abu Dhabi to discuss a rescue plan for a post-conflict Syria similar to the Marshall Plan implemented in post-World War II Europe.
One of the opposition delegates to the working group, Farah Attasi, said a principal goal of the project was to prepare for rebuilding the Syrian state following a change of government.
The violence and the resulting Western sanctions have had a drastic impact on the Syrian economy.
Tourism has been decimated and the government says oil revenues have been slashed by nearly $4 billion.