The Interior Ministry, which oversees the police and security services, said 55 people were killed and more than 370 hurt. Officials said suicide bombers detonated explosives weighing more than 2,200 pounds.
World powers seeking to halt Syria's unrest condemned the attack and urged all sides to adhere to a cease-fire brokered by U.N. and Arab League envoy Kofi Annan.
"In order to prevent another escalation of violence, we continue to call on the Syrian regime to fully and immediately implement the Annan plan," State Department spokeswoman Victoria Nuland said in Washington.
The blast was the largest and deadliest yet in a series of bombings targeting state security buildings since December.
The government blamed the attack on terrorists it says are driving the uprising, which has grown into the strongest threat to the Assad dynasty in its four decades in power.
The Syrian Foreign Ministry sent letters to U.N. Secretary-General Ban Ki-moon and the head of the Security Council, asking the body "to take steps against states, parties and media outlets that practice and encourage terrorism," Syria's state news service said.
Syria's U.N. ambassador, Bashar Ja'afari, told the Security Council that a second bombing Thursday, in Aleppo, also killed civilians and damaged property.
The Britain-based Syrian Observatory for Human Rights said five intelligence officers were killed when a bomb targeted their car in Aleppo. It was unclear if this was the same incident.
There was no immediate claim of responsibility for the Damascus attack.
A leader of the Free Syrian Army, an umbrella group of anti-regime militias, condemned the attack and denied the group was involved.