The blasts Wednesday hit a main square near a military officers’ club in the city, which has seen increased fighting in recent days between government forces and rebels opposed to President Bashar al-Assad.
The opposition Syrian Observatory for Human Rights put the death toll at more than 40.
A pro-government television station broadcast video it said was the aftermath of the blasts. The images show extensive damage to several buildings with piles of rubble lying the street.
State media blamed terrorists for the bombings.
Meanwhile, the joint United Nations-Arab League envoy to Syria Lakhdar Brahimi is set to return to the region next week as he tries to revive efforts to end the 18-month conflict.
U.N. Deputy Secretary-General Jan Eliasson said Tuesday that Brahimi will be based in Cairo. He also said the U.N. wants to see a reduction in violence from Assad’s government, followed by similar efforts by the opposition.
In reports published Tuesday, Western news agencies quoted Lebanese sources and Syrian activists as saying that a senior commander and two other fighters from the militant group Hezbollah were killed near the Syrian town of Qusair. The reports said the men were killed in a Syrian rebel ambush on Saturday or Sunday.
Syrian rebels have accused Hezbollah of helping President Assad to fight the uprising against his autocratic rule. The group has maintained strong political support for the Syrian president but has not admitted to any military activity inside Syria.