The fighting comes after claims by Syrian state television of at least three deaths due to opposition shelling of a district, and just two days after the Syrian army gained full control of Aleppo city.
At least six civilians were also killed on Saturday in air strikes on the rebel-held town of Atareb, west of Aleppo, according to the Syrian Observatory for Human Rights.
The SOHR, a UK-based information office that has been documenting human-rights abuses in Syria, said at least two children were among the dead.
The SOHR could not immediately specify who had carried out the air raids, but Russian and government warplanes typically carry out raids in Aleppo province.
An AFP correspondent in Atareb said military aircraft could be seen circling above the town and a nearby village throughout the day.
A reporting from Turkey’s Gazientep near the border with Syria, said the new wave of air strikes were concentrated on eastern, southern and northern outskirts of Aleppo, appearing to be aimed at keeping rebel forces away from the recaptured city.
“People are concerned because there are thousands of civilians who are still trapped on the outskirts of Aleppo, particularly those who have been evacuated from eastern Aleppo,” he said.
“If the fighting continues, that could further exacerbate the situation.”
Russia launched its air war in support of President Bashar al-Assad’s forces in September 2015, marking a major turning point in the government’s fight against armed opposition groups.