PPS said that Israeli military forces detained five Palestinians during the large military operation in Obwin village, north of Ramallah, where soldiers killed Omar Abu Laila, alleged Ariel attacker.
Governor Kamel Hmeid said Israeli troops in the adjacent village of Al Khader fired at a auto and wounded the driver late on Wednesday night.
Ahmad Manasra was in the auto behind and got out of his vehicle to help the wounded man, but was shot in the abdomen.
It said in a short press statement that a Palestinian was shot in the chest and shoulder by Israeli soldiers as he was in a vehicle at an Israeli army roadblock at the entrance to Bethlehem.
"This is a summary execution and Israel bears the full responsivity for this crime", Hmeid said.
The Israeli military said it was checking the report.
It gave no details about the circumstances of the night-time shooting.
A Palestinian was killed by Israeli gunfire in the occupied West Bank, Palestinian medics said, and the military announced on Thursday that a soldier had discharged his weapon and it was reviewing the incident.
Commenting on the Bethlehem-district raid, security sources said that the Palestinian was detained from Aida refugee camp.
On Sunday, a suspected Palestinian assailant fatally stabbed a soldier at an intersection on a busy West Bank highway and opened fire at the scene using the conscript's rifle, killing an Israeli rabbi and wounding a second soldier. "I don't know why they shot him".
Residents check a damaged house where a Palestinian gunman was killed by Israeli forces, in Abwein village, in the Israeli-occupied West Bank.
The uptick in West Bank violence comes as Israel is now in the midst of an election campaign and Egypt is trying to broker a long-term truce between Israel and Gaza's Hamas rulers.