The Syrian Observatory for Human Rights reported least 31 people were killed by the bomb, while a pro-government television station said 35 people were killed, foreign media outlets reported.
The bomb exploded near the headquarters of President Bashar Assad's ruling Baath Party and the Russian Embassy, the New York Times reported.
The Syrian Observatory for Human Rights said the dead were mainly civilian but that security forces were among the dead.
China's state-run Xinhua News Agency reported 237 people were injured.
Witnesses and state media said a suicide car bomber detonated himself at a crowded intersection near a mosque the Baath party headquarters.
State-run television and the Syrian Observatory said mortar shells also exploded near the Syrian Army General Command, but there were no reported casualties from that site, the Times reported.
The Local Coordination Committees, an association of opposition groups, said at least 163 people were killed across Syria Wednesday, including 19 children and eight women.
The organization said most of the victims were from Damascus and its suburbs, where 96 people died, including 48 opposition activists said were killed in an air attack on Hamoria, CNN said.
Video of the purported attack was posted on YouTube. The regime has cracked down on media, largely preventing foreign news agencies from reporting on the fighting that began in March 2011 as protests against President Bashar Assad before devolving into civil war.
The state-run Syrian Arab News Agency blamed "terrorists" -- its term for anti-Assad rebels -- for two mortar rounds that hit a Damascus sports stadium, killing a soccer player, and wounding several other players and team staff.
CNN reported Syrian rebels warned Hezbollah militants to stop fighting on Assad's behalf or face a violent response.
A post on the Free Syrian Army's Facebook page reads:
"We [FSA] are announcing and warning that if Hezbollah will not stop shelling the Syrian lands, villages and civilians from inside the Lebanese territories within 48 hours of issuance of this statement, we will respond to the sources of fire by our hands and eliminate it from inside the Lebanese lands. Wishing from our people in [border city] Hermel to stay away from Hezbollah's rocket launchers and its military centers."
Lebanese news agency NNA reported ex-Lebanese information minister and lawmaker Michel Samaha and Syrian Maj. Gen. Ali Mamlouk were indicted on charges of planning to carry out terrorist acts, preparing explosives and transferring the material from Syria to Lebanon. The news agency said the explosives were meant to be put in public places in Lebanon to kill deputies, religious figures and political dignitaries
Mamlouk heads Syria's national security and is Assad's special security adviser.
The Free Syrian Army said it downed a government aircraft that launched strikes on Zamalka, CNN said.
Also Wednesday, government forces hit a rebel command center in a suburb east of the capital, injuring Sheik Zahran Alloush, a founder of the Liwaa al-Islam brigade, the brigade said in a statement.
Syrian Information Minister Omran al-Zoubi said Wednesday the government hoped for greater dialogue with the opposition, and was reaching out to Syrians at home and abroad, CNN said.
Zoubi said during a Baath party leadership meeting in Damascus the Assad regime would offer "guarantees and logistic tools for the opposition behind borders, to facilitate the participation of those who wish to take part in a profound, serious dialogue."