The attack came after ISIS suffered several setbacks in northern Syria against Kurdish forces over the past weeks. The city of Hassakeh is divided between Bashar Assad's forces and Kurdish fighters.
Redur Khalil, a spokesman for the Kurdish People's Protection Units, or YPG, said ISIS militants attacked government-held neighbourhoods on the southern edge of Hassakeh, and captured some areas.
Syrian state TV reported intense clashes inside Hassakeh's southern neighbourhood of Nashawi. According to the report, ISIS fighters killed several people they captured in the city, including the head of a military housing institution. It said the militants sustained many casualties, including the commander of the group who is a foreign fighter.
ISIS tried to storm the city earlier this month and reached its southern outskirts before facing strong resistance from Syrian government troops who pushed them away.
Car bombing in Kobani
Also Thursday, ISIS staged a new attack on the Kurdish town of Kobani, which famously resisted a months-long assault by the Islamic militants. The attack involved a suicide car bombing that wounded scores.
"A group of fighters deployed in some areas of Kobani. We are defending a position now," Ghalia Nehme, a commander with the Kurdish Women's Protection Units, told The Associated Press by telephone from inside the border town.
After months of bloody street fighting, the Kurdish forces in Kobani, which lies along the Syria-Turkey border, succeeded in pushing out ISIS militants earlier this year. That was a landmark victory against the IS, enabled in part by U.S.-led coalition airstrikes.
Two Turkish officials said Thursday's attack involved a suicide bomber who detonated his car near the border gate that separates Kobani from the Turkish town of Mursitpinar.
The first official, from the local governor's office, said that 41 wounded were taken across the border to a hospital in Turkey. Surveillance footage showed a fiery explosion rocking Kobani in the dim light of dawn, he said, adding that video came from one of the 24 cameras monitoring the border crossing.
The second official, who is with the district government, put the number of wounded at 43 and said that sporadic gunfire could still be heard from the other side of the border later in the morning as well. He said one person, a child, had been killed.
There was no immediate way to resolve the discrepancy between their reports. Both officials spoke on condition of anonymity because they were not authorized to talk to reporters.
Syrian state TV said the extremists crossed from the Turkish side of the border into Kobani, adding that are casualties. It gave no further details.