Loud blasts from rocket fire and heavy machineguns could be heard throughout the city into the evening as warplanes screeched above, the reporter said.
Qamishli is under the shared control of the Syrian regime and Kurdish authorities, who have declared zones of "autonomous administration" across parts of north and northeast Syria.
The clashes broke out between government forces and the local Kurdish police force, known as the Asayish, at a checkpoint earlier on Wednesday, a Kurdish security source told AFP.
"Then, the Kurdish People's Protection Units (YPG) joined on behalf of the Asayish and the pro-government National Defence Forces joined on the side of the regime," the source said.
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He said "a number of our comrades" had died but would not give a specific number.
The Syrian Observatory for Human Rights said four NDF fighters were killed and another 20 were arrested by Kurdish forces.
The Britain-based monitor said three Asayish members were also killed in the fighting and several others were wounded.
Syrian troops and seasoned Kurdish fighters have coordinated on security in Hasakeh province where Islamic State group jihadists have tried to advance.
But tensions have built up between the sometimes-rival authorities, often over their individual military conscription services.
Two NDF militiamen were killed in similar clashes in December.