Syrian state-run TV said the blast came during a meeting of Cabinet ministers and senior security officials in Damascus, which has seen four straight days of clashes between rebels and government troops.
The high-level assassinations could signal a turning point in the civil war as the violence becomes increasingly chaotic.
U.S. Defense Secretary Leon Panetta said the bombing showed that the bloodshed in Syria was "rapidly spinning out of control," and it was time for the international community to bring "maximum pressure" on Assad to step down and permit a stable transfer of power.
The Assad family has ruled Syria for four decades, creating an ironclad and impenetrable regime. Wednesday's attack was an unheard-of strike on the inner circle.
Syria's rebel commander, Riad al-Asaad, said his forces carried out the attack.
Although state-run TV said it was a suicide blast, al-Asaad said his rebel forces planted a bomb in the room and detonated it. All those involved in carrying out the attack are safe, he said.
"God willing, this is the beginning of the end of the regime," al-Asaad told The Associated Press in a telephone interview from his base in neighboring Turkey.
"Hopefully Bashar will be next," he added.
State-run TV confirmed the deaths of two officials: Defense Minister Dawoud Rajha, 65, a former army general and the most senior government official to be killed in the rebels' battle to oust Assad; and Gen. Assef Shawkat, the deputy defense minister and one of the most feared figures in Assad's inner circle. He is married to Assad's elder sister, Bushra.
An authority with direct knowledge of the situation said Hassan Turkmani, a former defense minister, also was killed. The authority asked that his name and profession not be used for fear of reprisals.
Interior Minister Mohammed Shaar was wounded and in stable condition, state-run TV said.
It was not immediately clear where Assad was; he gave no immediate statements on the attacks, although in the hours after the assassination, Syria's state-run TV said a decree from Assad named Gen. Fahd Jassem al-Freij as the new defense minister. Al-Freij used to be the army chief of staff.
Republican Guard troops surrounded the nearby al-Shami Hospital, where some officials were taken for treatment, witnesses said.
Damascus-based activist Omar al-Dimashki said large numbers of troops and plainclothes police were deployed in the streets after the explosion. Snipers took positions on high buildings in different neighborhoods, he added.
"More than 80 percent of shops in Damascus are closed. People are rushing home," he said.
The attack came two days before the beginning of the Muslim holy month of Ramadan, when observant Muslims abstain from eating, drinking and sex from dawn to dusk. Last year, anti-government protests sharply increased during Ramadan.
The last major attacks on regime figures and government buildings date back to the early 1980s, when members of the Syrian Muslim Brotherhood were waging a guerrilla war to topple the regime of Assad's father and predecessor, President Hafez Assad.
Hafez Assad himself survived an assassination attempt in 1980 when members of the Muslim Brotherhood threw grenades at him, wounding him in the leg.
The violence in Syria has spiked in recent months. Besides a government crackdown, rebel fighters are launching increasingly deadly attacks on regime targets, and several big suicide attacks this year suggest that al-Qaida or other extremists are joining the fight.
Activists say more than 17,000 people have died since the uprising began in March 2011.
The Syrian army said in a statement that its forces will continue to fight.
"Whoever thinks that by targeting the country's leaders they will be able to twist Syria's arm is disillusioned because Syria's people, army and leadership are now more determined than ever to fight terrorism ... and cleanse the nation from the armed gangs," it said.
Rajha was the most senior Christian government official in Syria, appointed to the post by Assad last year. His death will resonate with Syria's minority Christians, who make up about 10 percent of Syria's population and have mostly 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.
The blast came on the same day the U.N. Security Council was scheduled to vote on a new resolution aimed at pressuring the Assad regime to comply with a peace plan put forth by special envoy Kofi Annan.
But Russia remained at odds with the U.S. and its European allies over any mention of sanctions and Chapter 7 of the U.N. charter, which could eventually allow the use of force to end the fighting in Syria.
The state-run news agency SANA reported that the bombing was aimed at the National Security building, a headquarters for one of Syria's intelligence branches and less than 500 meters (yards) from the U.S. Embassy. The embassy has been closed since Washington withdrew its ambassador months ago.
Police had cordoned off the area, and journalists were banned from approaching the site.
Earlier, SANA said soldiers were chasing rebels in the Midan neighborhood, causing "great losses among them." The Britain-based Syrian Observatory for Human Rights said army helicopters attacked the neighborhoods of Qaboun and Barzeh.
Diplomacy so far has failed to stop the bloodshed, and there appeared to be little hope that the U.N. would unite behind a plan.
The key stumbling block is the Western demand for a resolution threatening non-military sanctions and tied to Chapter 7 of the U.N. Charter, which could eventually allow the use of force to end the conflict.
Russia is adamantly opposed to any mention of sanctions or Chapter 7.
AP writers Zeina Karam in Beirut and Albert Aji in Damascus, Syria, contributed to this report.
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