Residents told the British-based Syrian Observatory for Human Rights they saw bodies in the streets of Aleppo, but neither the opposition group nor official media gave numbers of casualties. The Observatory said the blast had been close to a state security office.
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State news channel Syria TV said the "terrorist" explosion had been between two residential buildings in the al-Suleimaniya district of Aleppo, behind a post office building.
The opposition reported heavy raids by security forces and fighting with rebels in northern and southern Syrian provinces and suburbs of Damascus.
In the capital, as crowds gathered for memorials to victims of Saturday's car bombs, security forces broke up an opposition march of more than 200 people when protesters began shouting "the people want to topple the regime".
The phrase has echoed through the wave of Arab uprisings that began last year and has toppled autocratic rulers in Tunisia, Egypt, Libya and Yemen.
"They were walking through an area in central Damascus, near SANA (the state news agency). At first they shouted slogans against violence and the police didn't do anything, but as soon as they started to call for regime change the police rushed in and started beating people with canes," said Rami Abdelrahman, from the Syrian Observatory for Human Rights.
The protest, which called for non-violent resistance to the government, had been led by moderate opposition leaders previously tolerated by the government because of their calls for dialogue and rejection of foreign intervention.
Activists said the Sunday march aimed to commemorate the peaceful roots of Syria's uprising, which has been overshadowed by a growing armed insurgency against state security forces.
Security forces arrested Mohammed Sayyed Rassas, a leader of the National Coordinating Body for Democratic Change (NCB), an opposition group which had visited China and Russia in attempts to promote dialogue between Assad and the opposition.
Most opposition groups have rejected the NCB over its insistence on non-violence and its stance against foreign intervention, arguing the government's fierce crackdown has made arming the uprising inevitable.
Police also briefly arrested Fayyez Sara, who headed the Committee to Revive Civil Society, other activists said.
Syrian government forces have crushed a rebel stronghold in the central city of Homs and have been pounding rebel strongholds in northern Idlib.
"It's clear that the battle is finishing in the regime's favor overall," said a Lebanese official close to Assad's government.
"On the security level there is a long and difficult struggle for the regime and it is obvious this will take a long time to finish ... We will see many more explosions like those we saw yesterday but in general they have finished off the military fight and they don't have much more to do."
The United Nations says more than 8,000 people have been killed by security forces in the crackdown on a revolt against four decades of rule by the Assad family.
The struggle has become increasingly bloody as peaceful protest has given way to rebellion by armed groups. Authorities say they are fighting foreign militants who have killed more than 2,000 members of the security forces.
Heavy fighting raged in the northwestern province of Deir Ezzor and military vehicles were torched, activists said on Sunday.
Rebels also blew up a bridge in southern Deraa, birthplace of the uprising, the Observatory said. The bridge had been used to transport supplies to security forces who surround the city.
The Observatory said security forces raided the town of Artouz, a Damascus suburb, looking for wanted men. The Local Coordination Committee said residents there could hear heavy gunfire.
In central Damascus, crowds of Syrians gathered at the sites of the two car bombings outside security bases on Saturday.
The state news channel Syria TV showed footage of charred apartments, shattered windows and debris.
Dozens of people waving Syrian flags gathered to pray for the victims.
"Whatever they want to do we won't be afraid," said one woman speaking to the channel. "We won't be afraid, we are with President Assad ... those who don't love Damascus should leave."
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