Activists said government forces had stormed Hajar al-Aswad, a southern suburb of Damascus, and that the situation for residents was desperate.
State media said troops had killed many of what they called “terrorists”.
Earlier, Amnesty International warned that indiscriminate air and artillery strikes were causing a dramatic rise in civilian casualties in Idlib and Hama.
The report said the plight of people in the two provinces had been under-reported because world attention had focused on Damascus and Aleppo.
Meanwhile, Iranian Foreign Minister Ali Akbar Salehi held talks with President Bashar al-Assad and other officials in Damascus.
Ali Akbar Salehi said a solution to the conflict, which the UN estimates has left at least 20,000 people dead, lay “only in Syria and within the Syrian family”.
Rebels have also taken full control of the Tal al-Abyad border crossing with Turkey after a lengthy battle with government forces overnight, according to Turkish officials and witnesses.
The crossing is further to the east than any of the others previously captured by rebels, and could make it easier for them to get fighters and ammunition in and out of Syria.
On Wednesday, opposition activists said the military was attacking the south-western Damascus suburbs of Muadhamiya, Jadidat Artouz and Kanakir, Qudsaya to the north-west, and the southern districts of Qaddam, Assali, Yalda and Hajar al-Aswad.
They posted videos online which they said showed helicopter gunships firing rockets on Hajar al-Aswad, as well as the bodies of some of the more than 20 people they said had been killed in the assault. The army was destroying and setting houses on fire, they added.
State media said troops had moved into Hajar al-Aswad and clashed with an “armed terrorist group” near a cemetery, eliminating “a number of its members”, and that others had been killed as streets were “cleansed”.
The Syrian Observatory for Human Rights, a UK-based activist group, later said rebel fighters had announced their withdrawal from Hajar al-Aswad, Qaddam and Assali after weeks of violent clashes.
Activists also reported that the bodies of at least 20 people executed by government forces had been found in the north-eastern district of Jobar.
In Aleppo, government forces had bombarded several central areas surrounding the Old City, including Bab al-Hadid and Bab al-Nasr, and also attacked the outlying districts of Hananu and al-Bab, they added.
The Local Co-ordination Committees, an activist network, said more than 62 people had so far been killed across the country on Wednesday, including 30 in Damascus. It put the death toll on Tuesday at 160.
The reports of violence came as Amnesty International said indiscriminate air attacks and artillery strikes by Syrian government forces are killing, maiming, and terrorizing civilians in the Idlib, Jabal al-Zawiya and north Hama regions.
Donatella Rovera, Amnesty’s senior crisis response adviser, who recently returned from northern Syria, said there was evidence that the army and air force were increasingly using battlefield weapons in residential areas where government troops had been forced out by opposition forces, with disastrous consequences for civilians.
“They are using in equal measure air-delivered, large, old, Soviet-era unguided bombs – free-fall bombs – the opposite of smart bombs,” she said.
“They are dropped over an area. There’s no way you can target them at a specific target or specific building.”
“They fall over people’s houses, over markets, in the street. Many of those who were killed and injured are children. Every day, in the field hospitals, on the ground, in the streets and in people’s homes I was seeing the disastrous consequences of these attacks on civilians.”
Amnesty’s report says the group carried out first-hand field investigations in the first half of September into attacks which killed 166 civilians, including 48 children and 20 women, in 26 towns and villages.
In a separate development, a Syrian general who defected to the opposition told the Times newspaper that the president had discussed using chemical weapons in the conflict, and even whether they should be transferred to the Lebanese Shia Islamist movement, Hezbollah.
“We discussed this as a last resort – such as if the regime lost control of an important area such as Aleppo,” General Adnan Sillu said.
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