A Kurdish-led alliance, backed by air strikes of the US-led coalition, has been battling to oust ISIS from the pocket in the eastern province of Deir ez-Zor since September.
But the Syrian Democratic Forces suffered a series of setbacks, including due to a vicious fightback by jihadists and bad weather that impeded visibility.
On Thursday, an SDF commander said the alliance had managed to break into the pocket and wrest part of its main town from ISIS.
"Heavy clashes are ongoing inside the town of Hajin, after our forces advanced inside and started to control some of its neighbourhoods," Redur Khalil told AFP.
The SDF opened up humanitarian corridors out of the beleaguered pocket, allowing more than 1,000 civilians -- mostly woman and children -- to flee from Hajin in the past few days.
Khalil accused ISIS of using civilians as human shields, and said the corridors would remain open.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said the SDF launched an attack on Tuesday and than dozens of families had managed to flee.
The attack was backed by the heaviest shelling and air strikes by the US-led coalition since the start of the offensive on the Hajin pocket on September 10, Observatory chief Rami Abdelrahman said.
Since Tuesday, 34 jihadists including three suicide bombers, and 17 SDF fighters have been killed in the fighting, the Observatory said.
In almost three months of battle, more than 820 jihadists and more than 480 US-backed fighters have been killed, the monitor says.
More than 300 civilians have been killed in that period, its says, though the coalition has repeatedly said it did not target non-combatants.
ISIS overran large parts of Syria and neighbouring Iraq in 2014, declaring a "caliphate" across territories it controlled.
But various offensives in both countries have routed the jihadists from most of that land, crushing their dreams of statehood.
In Syria, the jihadists retain a presence in the vast Badia desert that stretches to the Iraqi border, as well as the pocket under attack around Hajin.
"The liberation of Hajin will not signify the end of ISIS," Khalil said, warning it would retain sleeper cells. "Operations to expel them will still last a long time."
