According to the Syrian Observatory for Human Rights, the Syrian army backed by Russian air cover is trying to reach the al-Furat lake and the road connecting al-Raqqa with the province of Aleppo.
The fighting, which broke out on Thursday, has so far killed 26 IS militants and nine security forces.
If the army succeeds, the IS will be besieged by the Syrian army in the south and southwestern parts of Aleppo, while the US-backed Syrian Democratic Forces (SDF) rebels will be besieging the terror group from the west.
Meanwhile, the al-Qaida-linked Nusra Front, which along with the IS, unleashed an offensive against government troops positions in southern Aleppo and fired tens of improvised rockets on a predominantly-Kurdish district inside Aleppo.
Syria's national TV said over 40 people were killed Saturday by continuous rebel shelling against the Kurdish-dominated Sheikh Maksud district in Aleppo.
Aleppo, Syria's second largest city and once an economic hub, holds its significance due to its location near the Turkish borders.
Each party of the conflict is now fighting to consolidate positions, and claim more territory in that key area.