The Syrian Observatory for Human Rights, a Britain-based monitor, said regime forces had seized parts of Al-Nashwa district in southern Hasakeh, which IS fighters entered last Thursday.
But it said clashes were continuing around the neighbourhood with "shelling by both sides and air raids on the area where fighting is taking place".
A security source in Damascus confirmed that fighting was still ongoing in the district.
"In Hasakeh, combat is continuing today, and the army is pursuing Daesh wherever they find them," he said, using the Arabic acronym for IS.
He said "martyrs are still falling" in Hasakeh but gave no specific toll.
IS launched a new bid to take Hasakeh city, a provincial capital, last week, entering from the south and seizing two neighbourhoods.
The city is divided between the control of regime forces and Kurdish fighters, who have largely kept out of the latest round of fighting.
They have restricted their activity to defending the mostly northern neighbourhoods under their control.
The Observatory said today that IS forces had shelled several Kurdish-controlled districts in the city, but there were no initial reports of casualties.
Yesterday, three IS car bombs killed 12 Syrian troops and militiamen in the city, the Observatory said.
Nine IS fighters were also killed in yesterday's clashes with the regime, it added.
The army has brought in reinforcements in an attempt to expel the jihadists, as it has done during previous attacks.
IS has repeatedly sought to enter Hasakeh, including last month when it advanced to the southern outskirts before being pushed back in heavy fighting.
IS has captured around 50 per cent of Syria's territory since it emerged in the country in 2013.
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