A claim of responsibility was posted on Facebook by Liwa al-Islam, a rebel group. Translated as "The Brigade of Islam", it said in a statement that it "targeted the cell called the crisis control room in the capital of Damascus."
The Free Syrian Army also claimed responsibility for the attack, according to spokesman Qassim Saadedine. "This is the volcano we talked about, we have just started," he said.
Syrian opposition leader Kamal al-Labwani told al-Arabiya, a satellite channel, that a member of the rebel Free Syrian Army planted a TNT and C-4-based device inside the building ahead of the meeting, and then detonate the bomb remotely before fleeing to safety.
The capital has seen four straight days of clashes pitting government troops against rebels - an unprecedented challenge to government rule in the tightly controlled capital.
Rajha, a former army general, was the most senior Christian government official in Syria. Assad appointed him to the post last year.
His death will resonate with Syria's minority Christian population, who make up about 10 percent of Syria's population and have generally stood by the regime.
Christians say they are particularly vulnerable to the violence sweeping the country of 22 million people, and they are fearful that Syria will become another Iraq, with Christians caught in the crossfire between rival Muslim groups.
