Six people were killed in the blast, the British-based Syrian Observatory for Human Rights said. Previous rebel attacks on government targets included a December bombing which wounded Assad's interior minister.
As prime minister, Wael al-Halki wields little power but the attack highlighted the rebels' growing ability to target symbols of Assad's authority in a civil war that, according to the United Nations, has cost more than 70,000 lives.
Assad picked Halki in August to replace Riyadh Hijab, who defected and escaped to neighbouring Jordan just weeks after a bombing killed four of the president's top security advisers.
Monday's blast shook the Mezze district, sending thick black smoke into the sky. The Observatory said one man accompanying Halki was killed as well as five passers-by.
State television showed firemen hosing down the charred and mangled remains of a car. Close by was a large white bus, its windows blown out and its seats gutted by fire. Glass and debris were scattered across several lanes of a main road.
"The terrorist explosion in Mezze was an attempt to target the convoy of the prime minister. Dr Wael al-Halki is well and not hurt at all," state television said.
It later broadcast footage of Halki, who appeared composed and unruffled, chairing what it said was an economic committee.
In comments released by the state news agency SANA but not shown on television, Halki was quoted as condemning the attack as a sign of "bankruptcy and failure of the terrorist groups", a reference to the rebels battling to overthrow Assad.
Mezze is part of a shrinking "Square of Security" in central Damascus, where many government and military institutions are based and where senior officials live.
Sheltered for nearly two years from the destruction ravaging much of the rest of Syria, it has been sucked into violence as rebel forces based to the east of the capital launch mortar attacks and carry out bombings in the centre.
CHEMICAL WEAPONS
Assad has lost control of large areas of northern and eastern Syria, faces a growing challenge in the southern province of Deraa, and is battling rebels in many cities.
But his forces have been waging powerful ground offensives, backed by artillery and air strikes, against rebel-held territory around the capital and near the central city of Homs which links Damascus to the heartland of Assad's minority Alawite sect in the mountains overlooking the Mediterranean.
As part of that counter-offensive, Assad's forces probably used chemical weapons, the United States and Britain have said.
However the trans-Atlantic allies, whose 2003 invasion of Iraq to overthrow Saddam Hussein was based in part on flawed intelligence about an Iraqi programme of weapons of mass destruction, have been cautious in their accusations.
Despite congressional pressure on Barack Obama to do more to help the rebels, the U.S. president has made clear he is in no rush to intervene on the basis of evidence he said was preliminary.
Britain, which says there is limited but growing evidence of chemical weapons use, said it wanted a United Nations investigation to see "whether or not there is verified use of chemical weapons".
"We've been very clear that, should that be the case, then the repercussions would be serious," British Foreign Office Minister Alistair Burt said during a visit to Beirut.
"That is why it is so important to have this independently verified and for the U.N. to do their investigation".
A U.N. team of experts has been waiting to travel to Syria to gather field evidence, but has yet to win agreement from Syrian authorities who want it to investigate only government accusations of chemical weapon use by rebels in Aleppo province.
Russia, which has criticised Western and Gulf Arab support for the anti-Assad fighters, said that attempts by Western countries to expand the U.N. inquiry to cover rebel accusations of Syrian government use of chemicals in Homs and Damascus mounted to a pretext to intervene in the civil war.
"There is not always a basis for the allegations (of the use of chemical weapons)," Russian Foreign Minister Sergei Lavrov told a news conference.
"There are probably governments and a number of external players who believe that it is fine to use any means to overthrow the Syrian regime. But the theme of the use of weapons of mass destruction is too serious and we shouldn't joke about it. To take advantage of it (to advance) geopolitical goals is not acceptable."
The United Nations said in February that around 70,000 people had been killed in Syria's conflict. Since then activists have reported daily death tolls of between 100 and 200.
Five million people have fled their homes, including 1.4 million refugees in nearby countries, and financial losses are estimated at many tens of billions of dollars.
The Beirut-based U.N. Economic and Social Commission for Western Asia estimates that 400,000 houses have been completely destroyed, 300,000 partially destroyed and a further half million have suffered some kind of structural damage.
