Abdul Qader Zaqdah, 25, was gunned down when residents clashed with their own security forces, who arrived to remove barricades and explosives set up to block Israeli forces from conducting raids.
The circumstances of the death were not clear, with some reports saying he was caught in the crossfire.
“The Palestinian Authority and its security apparatus are expressly forbidden from entering the Tulkarem camp and will be dealt with by bullets as the occupation forces are treated,” the Al Aqsa Martyrs' Brigades, the armed wing of the ruling Fatah party, said.
Gaza-based Hamas, a rival of Fatah, also condemned the killing, demanding punishment for those “shooting at civilians and hunting down resistance fighters”.
Palestinian police spokesman Luay Arzeikat said an investigation is under way.
Speaking to The National, Palestinian Authority security forces spokesman Talal Dweikat said it was “unclear” who shot Zaqdah.
“Either way it is very sad when a Palestinian is killed by another, whether by security forces or not," he said.
Mr Dweikat maintains that security forces were removing “suspicious devices” after receiving complaints from civilian groups about the dangers posed by improvised explosives resistance groups had placed near schools.
Videos shared by militant groups on Telegram were purported to show Palestinian Authority security forces cracking down on people outside the hospital where Zaqdah's body was kept.
Palestinians have long accused the Palestinian Authority of working with Israeli security forces during raids, including one in Jenin in July where at least 17 people were killed and 80 others were wounded.
Armed groups criticised Palestinian forces failing to stop the raid and earlier told The National that president Mahmoud Abbas was not supportive of them in their time of need.