Control of Aleppo city -- Syria's pre-war economic hub -- has been divided since mid-2012, with government forces controlling the western part of the city while much of the surrounding province is held by rebel groups, ranging from Nusra and others in the west to the Islamic State group (IS) in the east.
The front lines there and in the surrounding countryside have long been static.
On Saturday, three senior Nusra members, one of them a US-designated "global terrorist", were killed in an air strike in Aleppo province on Thursday, a monitoring group said.
And regime troops seized at least five villages and several strategic hilltops on Saturday, bringing them to the edges of Al-Hader, just south of Aleppo city, the Britain-based Syrian Observatory for Human Rights said.
- Russian air raids -
Taking the village would provide the government a key supply route between Aleppo and the central province of Hama, according to Observatory director Rami Abdel Rahman.
He said that over the previous 24 hours, 17 rebels and eight pro-regime fighters had been killed, while around 2,000 families had fled the fighting. In all, he said, more than 250,000 people had been killed since the start of the Syrian conflict in 2011.
A Syrian military source, meanwhile, said troops were also advancing on Kweyris military airport east of Aleppo city, which has been under siege by IS fighters.
If the army secures the air base, it could be used by Russian planes -- currently flying out of the Hmeimim base in Latakia province on the Mediterranean coast -- to launch strikes, the Observatory said.
The offensive comes with Russian warplanes having carried out at least 80 air raids on the region since Friday morning, according to an activist, with both Moscow and Tehran stepping up their support for Damascus.
A US official said as many as 2,000 fighters from Iran and its regional allies were supporting the Syrian army's offensive in coordination with Russia, while Iranian Deputy Foreign Minister Hossein Amir Abdollahian pledged Tehran would step up its military support for the regime.
- 'Defending national interests' -
Russian Prime Minister Dmitry Medvedev said Moscow's air war was an attempt to protect its own national interests and security, amid reports that thousands of fighters from the former Soviet Union are fighting with IS in Syria.
"Of course we are not fighting for specific leaders, we are defending our national interests, on the one hand," Medvedev said.
"And secondly, we have a request from the lawful authorities (of Syria). That is the basis we are working on," he said.
"The president (Vladimir Putin) said this: it's obvious that if we don't destroy these terrorists there, they will come to Russia."
Russia's military said it was continuing to use its drones over Syrian territory, despite suspicions that one was downed by Turkey on Friday. The defence ministry said its latest strikes in Syria hit 49 targets in Hama, Idlib, Latakia, Damascus and Aleppo provinces.
In Moscow on Saturday, around 200 people demonstrated against Russia's air campaign, with police arresting one woman with a banner reading, "Putin assassin, don't bring shame on Russia".
Syria's opposition coalition has also called for "urgent action to put an end to the Russian aggression".
And despite the regime push in Aleppo, they faced resistance in the central province of Homs.
Government forces have been trying to seize a rebel-held village in an enclave north of Homs city, which is controlled by the regime.
The Observatory said Saturday nine Russian air strikes had struck the village and its surroundings, where regime forces were locked in heavy fighting despite the air support.