Television footage and photos have shown smoke billowing from the explosion sites, twisted steel and debris strewn in front of a blasted-out building, and the mangled remains of victims.
There was no immediate claim of responsibility, but Syrian officials blamed "terrorists" who may be linked to the year-long protests against President Bashar al-Assad.
The explosions occurred a day before a team of U.N. experts were due to begin a trip to Syria to discuss the possible deployment of international monitors, as part of efforts to curb deadly violence from the government's crackdown on dissent.
After briefing the U.N. Security Council Friday, former U.N. chief Kofi Annan said Syria's political turmoil needs to be handled carefully to avoid any "miscalculations" that could lead to a "major escalation" that could affect the entire region.
Annan is serving as a special U.N.-Arab League envoy to Syria. He traveled to Damascus about a week ago and discussed proposals with Assad on ending Syria's political turmoil.
The U.N. says more than 8,000 people have died since the anti-government uprising began a year ago.
Syria's last major bombings were in February. Twin blasts at security facilities in the northern city of Aleppo killed 28 people.