Hundreds of Syrians fled Hassakeh on Friday as violence escalated between the Syrian Democratic Forces (SDF) and Islamic State militants.
More than 100 IS fighters, using heavy machine guns and vehicles rigged with explosives, attacked a prison in the city on Thursday night.
Gweiran Prison is believed to house some 3,000 suspected IS militants.
A spokesperson for the Kurdish-led SDF said seven US-backed Kurdish fighters were killed and several others were wounded.
At least 23 IS attackers were also among the dead, he said.
A Syrian opposition war monitor had a higher death toll, saying a total of 67 people were killed in the battle.
The SDF said more than 100 militants who escaped were arrested, while another group of inmates staged a new escape attempt on Friday.
The SDF spokesman also said IS gunmen also controlled several homes in the nearby neighbourhood of Zuhour.
The extremists had rigged several homes with explosives and were using civilians as human shields, he added.
The US-led coalition carried out an airstrike after reported casualties among the Syrian-led Kurdish forces late on Thursday.
Coinciding with the attack in north-eastern Syria, IS gunmen struck an army barracks in a mountainous area north of Baghdad early on Friday.
At least 11 soldiers were killed as they slept, Iraqi military and security officials said.
The separate attacks are believed to be some of the largest since IS lost the final sliver of territory it held nearly three years ago.
In recent months, IS sleeper cells have become more active in both countries, claiming attacks that have killed scores of Iraqis and Syrians.
AP
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