"We want revenge against Bashar and Maher," some shouted, in reference to the president's brother, who heads the feared Fourth Armoured Division.
Activists said the scattered protests were among the most widespread in Damascus of the 11-month uprising against the Assad regime inspired by the Arab awakening.
The protesters turned out after the UN General Assembly overwhelmingly backed an Arab League initiative calling on Assad to step aside, and ahead of a visit by a Chinese envoy pushing for peace.
Assad, in remarks to visiting Mauritanian Prime Minister Moulaye Ould Mohamed Laghdaf, said reforms have to be synchronised with a "return to peace".
The Syrian Observatory for Human Rights said 26 people were killed on Friday, one of them at a demonstration that was fired upon in the capital.
At least 10,000 people demonstrated in the southern town of Dael, in Daraa province, where the protest movement was born in March 2011, said the Britain-based monitor.
In Homs, rockets crashed into strongholds of resistance at the rate of four a minute, according to an activist, who warned the city faces a humanitarian crisis.
Thirteen of the dead were in the Homs district of Baba Amr.
"It's the most violent in 14 days. It's unbelievable -- extreme violence the like of which we have never seen before," said Hadi Abdullah of the General Commission of the Syrian Revolution.
"There are thousands of people isolated in Homs ... There are neighbourhoods that we know nothing about. I myself do not know if my parents are okay. I have had no news from them for 14 days," he told AFP by telephone.
A tank fired into a residential part of Homs, before bursts of machinegun fire clattered across the neighbourhood, a YouTube video showed.
"The regime troops are still shelling... but are reluctant to enter Baba Amr. They are on the periphery and are moving slowly. The army will lose if it begins urban warfare," activist Omar Shakir said later on Skype.
Human rights groups estimated the two-week assault on Homs has killed almost 400 people, and a medic reached on Skype said 1,800 have been wounded.
"There are injuries that cannot be treated because of a lack of medical equipment," Dr Ali al-Hazzuri told AFP. "There are casualties who are close to dying."
The violence came as US Secretary of State Hillary Clinton hailed an "overwhelming international consensus" against Damascus after the UN General Assembly voted on Thursday to demand an immediate halt to the crackdown.
The strongly worded resolution, adopted by a 137-12 vote, calls on Damascus "to stop all violence or reprisals immediately, in accordance with the League of Arab States initiative."
It was referring to a peace plan put forward by the pan-Arab bloc calling on Assad to hand power over to his deputy and for the formation of a unity government ahead of elections.
Russia, China and Iran opposed the non-binding resolution. The vote came just days after Beijing and Moscow vetoed a similar resolution at the UN Security Council.
The vote "demonstrated an overwhelming international consensus that the bloody assaults must end," Clinton said at a press conference with EU foreign policy chief Catherine Ashton.
"In the face of this global condemnation, the regime in Damascus, however, appears to be escalating its assaults on civilians, and those who are suffering cannot get access to the humanitarian assistance they need and deserve," she said.
"So we will keep working to pressure and isolate the regime, to support the opposition and to provide relief to the people of Syria."
France and Britain pledged to help the opposition in its struggle against Assad's regime but said conditions were not right for a foreign intervention, as in Libya.
Meeting for a summit in Paris, French President Nicolas Sarkozy and British Prime Minister David Cameron expressed support for a conference to form an international coalition in Tunis next week dubbed the Friends of Syria.
"We cannot accept that a dictator massacre his own people, but the revolution will not be brought from outside, it will rise from inside Syria, as it has done elsewhere," Sarkozy told a joint news conference.
"What is happening in Syria is appalling, for the government to be butchering and murdering its own people," Cameron said.
The two said France and Britain were working together to help the opposition, with Sarkozy urging anti-Assad forces to unite and be better organised.