Dozens of air strikes hit near the town of Khan Touman, which rebels took from forces loyal to the government and its ally Iran late on Thursday, insurgents and state media reported.
Aleppo – one of the biggest strategic prizes in a war now in its sixth year – has been divided into government and rebel-held zones through much of the conflict. The surrounding region is also crossed by valuable supply routes into neighbouring Turkey.
The Syrian army said it had hit what it described as terrorist groups hard on Sunday, but did not give details of any territorial gains.
Manar, the media outlet of the Iran-backed Hezbollah group supporting Syrian government forces in the area, said heavy fighting was going on against the hardline rebels.
Government forces had made significant advances in the northern region after their other main ally, Russia, entered the war in September.
But the seizure of Khan Touman on Thursday by an alliance of Islamist insurgents known as Jaish al-Fatah, including the al Qaeda-linked Nusra Front, marked a major counter-attack by forces opposed to President Bashar al-Assad.
The loss of the town south of Aleppo was a particular blow for Iranian troops who suffered one of their biggest single-day losses in the conflict.
A fighter from the Nusra Front – which is not involved in a shaky ceasefire across Syria – said on social media it was now pushing further south towards the town of al Hader, a stronghold for Hezbollah and Iranian forces.
Inside Aleppo, where Russia said it extended a truce that began on Wednesday until Monday, rebels said the Syrian army shelled and bombed overnight their posts near a frontline in the western part of the city near the Jamiyat al Zahraa neighbourhood.
“We don’t know how to take cover from the intensity of rockets and air strikes that are showering us,” said Ahmad al Wawi, a fighter from Jaish al Mujahdeen.
Rebels are seeking to take over the area that would allow them to enter the heart of government-held parts of Aleppo.
The British-based Syrian Observatory for Human Rights said rebels fired rockets on residential areas in government-controlled areas and in the main Saad al Jabiri square injured seven, with reports of more casualties in the collapse of a building in Midan district which was hit by a missile.
In the western Aleppo countryside in the rebel-held town of Kafrnaha, a air strike hit a hospital with several killed, the Observatory said.
Separately Amaq news agency, which is associated with Islamic State, said the group had destroyed a gas plant in the desert outside the central city of Palmyra on Sunday.
Islamic State militants retreated from the ancient city two months ago but continue to operate in the surrounding area.
The Syrian war, which started with largely peaceful protests against the government, had descended into a sectarian war that has pulled in regional and global powers, killed at least 250,000 people and displaced half its pre-war 22 million population.