The government assault came a day after U.N. Secretary-General Ban Ki-moon said he had received "grisly reports" that President Bashar al-Assad's troops were executing and torturing people in the city after rebels abandoned their positions there.
"In an act of pure revenge, Assad's army has been firing mortar rounds and ... machine guns since this morning at Jobar," said the Syrian Network for Human Rights, naming a district next to Baba Amro, where rebels held out against almost a month of siege and shelling before fleeing this week.
"We have no immediate reports of casualties because of the difficulty of communications," the campaign group said in a statement.
Syria's government says it is fighting foreign-backed "terrorists" whom it blames for killing hundreds of soldiers and police across the country.
The United Nations says Syrian security forces have killed more than 7,500 civilians since a revolt against Assad's rule began in March last year.
Concern was mounting for civilians in freezing conditions in Baba Amro, where International Committee of the Red Cross (ICRC) trucks were being held up by Assad's forces.
Anti-government activists said they feared troops wanted to prevent the ICRC witnessing a reported massacre of rebels in Baba Amro, which had become a symbol of the year-long uprising.
A Damascus-based ICRC spokesman said Syrian authorities had given the convoy permission to enter but government forces on the ground had stopped the trucks because of what they said were unsafe conditions, including "mines and booby traps".
"There has been fighting there for at least a month. The situation cannot be good. They will need food, it's cold, they will need blankets. And there are injured there that need to be evacuated immediately," Saleh Dabbakeh told Reuters.
Syrian state television broadcast interviews with unnamed civilians in what it said was the stricken district, against a backdrop of empty streets, some with heavy conflict damage.
"Anyone who went out on the street was kidnapped or slaughtered. We called for the army to come in. God bless the army, they saved us from the armed terrorist gangs," said one interviewee, referring to the Free Syrian Army (FSA) rebels.
The outside world has proved powerless to halt the killing in Syria, where repression of initially peaceful protests against Assad's rule has spawned an armed insurrection by army deserters and others.
Russia and China have twice vetoed council resolutions that would have condemned Damascus, accusing Western and Arab nations of pushing for Libya-style "regime change" in Syria.
China urged both Damascus and the rebels to end the violence immediately and start talks, but again said it opposed any foreign military intervention in Syria.
"We oppose anyone interfering in Syria's internal affairs under the pretext of 'humanitarian' issues," said a foreign ministry statement carried by Xinhua news agency early on Sunday Beijing time and monitored in London.
Former Syrian ally Turkey said Assad was committing "war crimes" and condemned Syria for blocking aid to Baba Amro.
"The Syrian regime is committing a crime against humanity every day," Turkish Foreign Minister Ahmet Davutoglu said.
British Foreign Secretary William Hague said his government was again seeking to have the U.N. Security Council tackle the Syrian crisis.
"This means working with other countries such as Russia and China that have blocked previous initiatives," he told Sky News.
The United States is drafting a legally binding council resolution that would call for aid workers to be allowed into besieged towns and an end to the violence, U.N. envoys said.
Syria's SANA news agency reported a suicide car bombing in the southern town of Deraa, but activists denied it was a suicide attack.
SANA said the Deraa bomber killed three people and wounded 20 others, while residents said seven people had been killed.
Elsewhere in Syria, anti-Assad activists reported mass arrests and the killing of six soldiers.
Campaigners said seven people had been killed in Syria's north, and three had been shot dead in east Syria's Deir al-Zor when troops opened fire on a funeral for two killed in a crackdown on democracy protests.
Senior rebel FSA officer Colonel Malik Kurdy said his fighters had seized an arms cache in a battle in countryside north of Damascus and killed and wounded about 100 Syrian troops, but added the report was preliminary.
Rights group Human Rights Watch distributed satellite images of Baba Amro that it said showed widespread destruction.
"The bombardment has severely restricted movement and relief efforts and deprived thousands of civilians of the ability to access the most basic commodities," it said in a statement.
Rami Abdelrahman, head of the Britain-based Syrian Observatory for Human Rights, said anti-Assad fighters had killed six soldiers and wounded nine in the town of al-Herak, south of Deraa.
He also said seven people had been killed in Syria's north in and around Idlib province, three by a roadside bomb and the others by gunfire from Syrian security services.
In the suburbs of Damascus, activists reported hundreds of arrests and said Syrian security forces had killed three people during raids in which they also set alight homes and cars.
Due to media restrictions, the activists' reports could not be independently verified.
In unusually tough remarks to the 193-member U.N. General Assembly on Friday, Ban explicitly blamed Damascus for the fate of civilians in the conflict.
"The brutal fighting has trapped civilians in their homes, without food, heat or electricity or medical care, without any chance of evacuating the wounded or burying the dead. People have been reduced to melting snow for drinking water," he said.
"This atrocious assault is all the more appalling for having been waged by the government itself, systematically attacking its own people."
Syrian U.N. Ambassador Bashar Ja'afari, said Ban's comments included "extremely virulent rhetoric which confines itself to slandering a government based on reports, opinions or hearsay."
Western diplomats on Saturday received the bodies of American journalist Marie Colvin and French photographer Remi Ochlik, who were killed on Feb. 22 during shelling of Baba Amro.
The diplomats, believed to be the French ambassador to Syria and a representative from the Polish embassy, which is managing U.S. affairs in Syria, had taken the bodies from the Al-Assad University Hospital in Damascus.
