The president's family belongs to the country's minority Alawite sect, who are largely driven by fears that they could be overwhelmed should al-Assad lose power, according to the president's uncle Rifaat. Recent reports, however, suggest discontent even within the minority community over his handling of the crisis.

Al-Assad's youngest brother, Maher, is thought to be Syria's second-most powerful man, overseeing two of the army's strongest units: the Republican Guard, which protects the regime in Damascus, and the elite Fourth Armored Division, which suppressed the early uprisings in southern Syria.

But on Wednesday, a rebel attack killed Defense Minister Dawood Rajiha; Deputy Defense Minister Assef Shawkat -- al-Assad's brother-in-law; and Hasan Turkmani, al-Assad's security adviser and assistant vice president, according to state television.

Shawkat was once in charge of the army's intelligence services and was said to be one of the president's closest allies.

Due to a translation error, an earlier version of this article erroneously reported that Interior Minister Ibrahim al-Shaar had been killed as a result of Wednesday's explosion at a national security building in Damascus. Al-Shaar was injured in the blast, but he is alive and in stable condition, according to Syrian state television. CNN regrets the error.

Wednesday's attack occurred during a meeting of ministers and security officials and was coordinated by rebel brigades in Damascus, opposition groups say.

Al-Assad quickly named Gen. Fahd Jassem al-Freij as defense minister, according to the state-run news agency SANA.

State media also reported that authorities have killed or captured a "large number" of terrorist infiltrators in Damascus and inflicted "heavy losses" on terrorists in Homs and Idlib.

But video from a Damascus suburb showed Syrians rejoicing after news spread of the bombing.

Meanwhile, reports of deaths across the country occur almost every day, with a London-based opposition group reporting last week that government forces carried out a massacre in Hama province, killing 220 people there.

Al-Assad's administration has consistently said that its forces are targeting armed terrorists funded by outside agitators.

In early July, al-Assad told a German television station that a months-old peace plan aimed at ending the violence hasn't failed, but rather has yet to be implemented because foreign countries are supporting "terrorists."

Former United Nations Secretary-General Kofi Annan, named as a special envoy to the region, has spearheaded the peace effort.

The president's remarks came on the same day that U.S. Secretary of State Hillary Clinton held that the days for the Syrian regime are numbered.

Noting recent defections, Clinton said, "The sand is running out of the hourglass."