According to activists with the Syrian Local Coordination Committee (LCC), seven civilians died in the city's Bab Amro neighborhood. One of those dead was reportedly an 8-year-old child.
This information could not be independently verified, however, and other reports gave lower casualty figures.
Witnesses cited by Reuters described heavy machinegun and anti-ancraft gun fire, as well as sniper shots from rooftops and checkpoints.
One activist told the news agency:
"We slept late because there were overnight street rallies celebrating the Arab initiative. This morning we woke up to rain and shelling."
Video footage purportedly shows the tank attacks:
The LCC also reported filming tanks driving through the streets of Damascus on Thursday.
The Syrian government agreed Wednesday to withdraw tanks from cities and halt violence against protestors as part of a peace deal set out by the Arab League.
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But opponents of the regime were sceptical that President Bashar al-Assad would stick to the agreement, accusing him of stalling tactics.
"This regime is notorious for maneuvering and for giving promises and not implementing any of them."
Activists say that demonstrations continued Thursday across Syria, including in Hama, Idlib, Deraa and Lattakia.
The LCC is also calling for renewed protests Friday:
"May tomorrow, Friday, be the day where all streets and squares become platforms for demonstrations and for the peaceful struggle towards achieving the downfall of the regime."
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