At least 170 people are reported to have been wounded in the twin blasts.
Early reports said that one blast was caused by a truck rigged with explosives.
Qamishli has regularly been targeted in bomb attacks, many of which have been claimed by the Islamic State group.
The IS-linked Amaq agency reported that a "suicide bomber in a truck bomb hit the headquarters of the Kurdish" forces in Qamishli, without explicitly claiming the attack as an IS operation.
However, IS apparently later claimed the attack, according to a state TV report cited by CNN.
An AFP reporter in the city said that the first explosion was caused by a suicide bomber who blew himself up inside a large truck by a checkpoint near local Kurdish adminstration ministries.
A source in the Kurdish Asayesh security forces told AFP "this is the largest explosion the city has even seen."
He added that local hospitals had been flooded with casualties from the attack.
Syrian state television meanwhile carried an appeal from the governor of Hasakeh province, where Qamishli is located, urging residents of the city to "go to public and private hospitals to donate blood for the victims of the terrorist bombings."
Explosion on Syrian-Turkish border, over 40 killed
27 July 2016
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.jpg "Explosion on Syrian-Turkish border, over 40 killed")
At least 44 people were killed in a double bombing in the Kurdish-majority city of Qamishli in northeast Syria on Wednesday, state TV said, as reported by the AFP news agency.
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