Tens of thousands of people have protested across Syria, days after the bloody crackdown on the city of Hama where the opposition had taken control.
Video said to be of Damascus showed crowds in a central district chanting: "Hama, we are with you until death" and "[President] Bashar [al-Assad] leave".
Security forces shot dead at least 13 protesters on Friday, reports say.
The US, German and French leaders have accused Mr Assad of "indiscriminate" violence against civilians.
The White House said President Barack Obama, Chancellor Angela Merkel of Germany and French President Nicolas Sarkozy had spoken in separate telephone calls, and warned of unspecified new measures against the Syrian leader.
In a broadcast from Hama, Syrian state TV said the city was under government control. Hama residents and human rights groups accuse the army of killing more than 100 civilians in a bombardment of the city, which has become a focus of the protests against Mr Assad's rule.
As many as 2,000 people may have been killed by security forces since opponents of President Assad's autocratic rule took to the streets in March.
Protesters were inspired by the successful uprisings in Tunisia and Egypt. Mr Assad has promised reforms, but blames the violence on "armed criminal gangs" backed by unspecified foreign powers.
Access to events in Syria has been severely restricted for international journalists and it is rarely possible to verify accounts by witnesses and opposition activists.
Marching in the heat
Activists had called for more protests after prayers on Friday, with one web user posting a message saying: "God is with us, are you?"
Video posted by activists purports to show protesters marching through the Midan district of the Syrian capital, close to the Old City.
Clapping their hands, they chanted: "We don't want you Bashar."
In another district of the capital, Qadam, protesters carried a banner reading: "Bashar is slaughtering the people and the international community is silent."
Security forces opened fire with live ammunition and tear gas in several cities, activists said.
At least 10 people were killed in the Damascus suburbs of Irbin, Moaddamia and Dumeir, and three in the city of Homs.
Abdel Karim Rihawi, head of the Syrian League for the Defence of Human Rights, told AFP news agency that 30,000 people had marched in the city of Deir al-Zour despite extreme heat.
Numbers were down on previous Fridays, when hundreds of thousands turned out for protests. Correspondents say this is probably because it was the first Friday in the holy month of Ramadan, when Muslims fast from dawn until dusk and go outside less.
Earlier, US Secretary of State Hillary Clinton accused security forces of killing some 2,000 people since March.
Residents of Hama, which has become a focal point of protests, told reporters that there had been more gunfire and shelling early on Friday.
Snipers and tanks have been firing on civilians and food and medicine supplies are running low, witnesses say.
But the Syrian TV report showed pictures of armed men hiding behind cars and claimed the army had quelled a rebellion.
The report showed deserted streets with flimsy barricades and piles of rubble. Later, the reporter went into buildings that appeared to have been destroyed in an explosion.
The UN Security Council issued a statement this week condemning the crackdown.
Russia, traditionally an ally of Syria, also joined the criticism, with President Dmitry Medvedev saying Mr Assad would "face a sad fate" unless he urgently carried out reforms and reconciled with the opposition.
The BBC's Jim Muir in neighbouring Lebanon says Mr Medvedev's statement may give the government pause for thought, but there has been no change in the attitude on the ground.