State TV said President Assad's brother-in-law, Assef Shawkat, and Gen Dawoud Rajha, the defence minister were victims of a blast during a high level security meeting. The Interior minister was also injured.
Gen Shawkat was the deputy defense minister and was among the most feared figures in Assad's inner circle. He is married to Assad's elder sister, Bushra.
Reports said the officials had been killed by a bodyguard in a suicide bombing in the capital of Syria but other reports said a device was placed within the building. A "terrorist bomb" which exploded at a national security building in Damascus during a meeting of ministers and security officials wounded several people, some of them critically, state television said.
Journalists are refused access to the National Security headquarters in Rawda, a high security district in the heart of the capital, Damascus (AFP/Getty Images)
The state-run news agency SANA reported that Wednesday's blast took place at the National Security building, a headquarters for one of Syria's intelligence branches. Activists in Damascus said by telephone that Republican Guards sealed off the Shami hospital in the capital after ambulances had brought casualties from the site of the explosion.
"The terrorist suicide bombing" came in the high security Rawda district in the heart of the capital as battles raged in Damascus for the fourth consecutive day.
There were "badly wounded" among ministers and officials, the broadcaster said.
Gen Shawkat was the deputy Minister of Defense of Syria since September 2011. He previously served as the army’s deputy chief of staff from July 2009 to September 2011.
Gen Shawkat was considered one of the president’s top security chiefs, however, he was replaced in 2010 as head of Military Intelligence and made deputy chief-of-staff of the armed forces.
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.
Gen Hisham Ikhtiyar, head of National Security, were among those listed as wounded in the bombing, which came in the midst of an offensive launched by rebels to capture Damascus. There were conflicting reports about the fate of the Interior minister, Mohammed al-Shaar
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.
Columns of black smoke rose over the capital, with the Local Coordination Committees, which organises anti-regime protests on the ground, reporting that Qaboon and Barzeh neighbourhoods were bombarded by loyalist forces.
It also said there was less traffic than normal in the city where fighting has raged since Sunday, with the rebels announcing a full-scale offensive dubbed "the Damascus volcano and earthquakes of Syria."
Regime forces and the FSA clashed in the Al-Midan and Zahira districts of Damascus as well as at Assali south of the city.