Images of charred bodies lying next to mangled vehicles were broadcast by state television channel Al-Ekhbariya, which said children among those wounded, as the blast occurred near a school the central Damascus district of Mazraa.
"At least 31 people were killed and dozens wounded, the majority civilians," said the Syrian Observatory for Human Rights, while the state news agency SANA reported 16 killed and 200 hurt in what it said was a suicide bombing.
The car bomb exploded at the 16 November Square near the Al-Iman mosque, next to the head offices of the Baath party, which has been in power for half a century.
Buildings were shattered by the blast, which sent thick black smoke billowing across the capital's skyline and all roads in the area were quickly sealed off, an AFP correspondent said.
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Ambulances sirens rang out, and machine gun fire was also heard in the area, as firemen rushed to the scene to douse the flames.
"It is terrorism... Is that what you call Islam?" one of the wounded told Syrian television.
"Is that the freedom you want? Is that the (rebel) Free Syrian Army?" said another man, speaking at the site of the attack.
The windows of the Russian embassy were blown out by the blast, but none of its staff were hurt, Russian news agencies reported.