The attack, which for the first time in a 16-month anti-regime uprising, targeted members of Assad's inner core, came hours ahead of a UN Security Council debate on Syrian sanctions, when a showdown between Western powers and Russia and China is expected.
Officials said the bomber struck as ministers and security officials were meeting at the heavily guarded national security headquarters in Damascus.
Defence Minister General Daoud Rajha and Assad's brother-in-law Assef Shawkat were killed and Interior Minister Mohammed al-Shaar and General Hisham Ikhtiyar, head of national security, were wounded, the channel and security officials said.
Syria's rebel Free Syrian Army (FSA) claimed responsibility for the deadly attack.
The FSA command "announces the good news of the outstanding operation this morning that targeted the national security headquarters and the killing" of the officials "responsible for barbaric massacres", it said.
The Syrian Observatory for Human Rights called Shawkat's death "a severe blow to the Syrian regime since he played the main role in operations by regular forces to crush the revolution".
State television reported that Assad had appointed Fahd al-Freij as new defence minister, while Syria's army vowed to "continue fighting terrorism".
"The terrorist act increases the armed forces' determination to clean the country of terrorist groups," it said.
Rajha, a Christian, was defence minister, deputy army chief and deputy head of the Council of Ministers. Assad himself is overall commander of the military.
Shawkat was deputy defence minister and a former military intelligence chief.
The national security branch, headed by Ikhtiyar, is a linchpin of Syria's security apparatus.
The brazen attack on regime insiders came as battles raged across Damascus and after the FSA – comprising defected soldiers and civilians who have taken up arms against Assad's forces – warned the government to "expect surprises".
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, the LCC said.
Rebel forces on Tuesday said the battle to "liberate" Damascus had begun, as heavy fighting raged with the regime using helicopter gunships in the capital for the first time.
'Victory is nigh'
FSA spokesperson Colonel Kassem Saadeddine had said on "victory is nigh" and the struggle would go on until the city was conquered.
"We have transferred the battle from Damascus province to the capital. We have a clear plan to control the whole of Damascus. We only have light weapons, but it's enough."
"Expect surprises," Saadeddine added.
Russia gave notice that it would not back a Western-backed UN resolution on the crisis as it would mean taking sides with a revolutionary movement.
"Now the Damascus Volcano, the battle for the capital and a decisive battle have been declared in Syria. Adopting the resolution would mean outright support of a revolutionary movement," Foreign Minister Sergei Lavrov said in Moscow.
British Foreign Secretary William Hague said by contrast that Syria is tipping into chaos and collapse, and that a strong UN Security Council stand is needed to push for the creation of a transition government.
"We are aware of reports that the Syrian Defence and Deputy Defence Ministers have been killed and a number of others injured by an apparent suicide bombing in Damascus," Hague said in a statement issued in London.
"This incident, which we condemn, confirms the urgent need for a Chapter VII resolution of the UN Security Council on Syria."
In Beijing, UN chief Ban Ki-moon urged the Security Council to act to stop the bloodshed in Syria, after holding talks ahead of a vote on fresh sanctions.
Ban said the Security Council must unite and take action on the "very serious" situation in Syria, after meetings with China's President Hu Jintao and Foreign Minister Yang Jiechi.
The Security Council will on Wednesday vote on a Western resolution renewing the UN mission in the country that calls for sanctions if the regime does not pull back heavy weapons.
China has twice joined Moscow during the 16-month conflict to block resolutions critical of Damascus.
Representatives of the Syrian National Council (SNC) – an umbrella opposition group – met ambassadors from the 15-nation Security Council, including Russian envoy Vitaly Churkin, to press them to back sanctions.
The current 90-day UN mission in Syria ends on Friday, and if no resolution is passed by then, it would have to shut down this weekend, diplomats say.
The Observatory, meanwhile, said at least 93 people were killed nationwide on Tuesday, among them 48 civilians, adding to its toll of more than 17 000 dead since the revolt erupted in March last year. – AFP