Dr Zaidoun al-Zoabi, head of the Union of Syrian Medical Relief Organisations, told the BBC that several villages he had visited were empty.
He saw thousands of people on the move, with no shelter or medical support.
The government offensive is the latest of at least four launched with Russian air support in the past two weeks.
Aside from the Aleppo countryside, they are taking place in mostly rural areas north of the cities of Homs and Hama, and in the rugged northern parts of Latakia province along the coast.
Rebel fighters - not including jihadist militants from Islamic State (IS) - had penetrated most of these strategically important areas earlier this year.
The government's losses prompted Russia to launch an air campaign to bolster President Bashar al-Assad in September, and also reportedly led Iran to deploy hundreds of combat troops. Tehran has previously only acknowledged sending military advisers.
'Sky filled with jets'
Dr Zoabi told the BBC's Newsday programme that he had seen thousands of people displaced by the fighting south of Aleppo in the past 72 hours.
"There are at least 70,000 people displaced from many, many villages in the southern, rural areas of Aleppo," he said. "I saw really thousands today on the move."
"We saw only people who do not have even tents, any shelter, whatever. People were asking for some food, sandwiches even," he added. "There is no medical support."
"The shelling is so fierce. The sky was filled with jet fighters, with helicopters and people are terribly scared. They are scared to death."
The Syrian Observatory for Human Rights said that government forces, backed by Syrian and Iranian militiamen and fighters from Lebanon's Hezbollah movement, had taken control of three hills near the town of Khan Tuman.
At least five people were killed in battles with al-Nusra Front, al-Qaeda's affiliate in Syria, and allied rebel factions, the UK-based monitoring group added.
Clashes were also reported in Aleppo's Bani Zaid and Salah al-Din districts.
On Sunday, Turkey's Prime Minister Ahmet Davutoglu warned that the offensive south of Aleppo, as well as attacks in the area by Islamic State militants, could "cause another wave of refugees".
More than 11 million Syrians have been driven from their homes since the uprising against Mr Assad began in March 2011.
More than 4.18 million have fled to neighbouring countries - 2.07 million of them to Turkey - with growing numbers now making the dangerous journey to Europe.
BBC News
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