TEL AVIV—A Palestinian driver rammed a car into a group of Israeli soldiers in Jerusalem, injuring 14 people, and clashes in the West Bank left two Palestinians dead, one of them a security officer, a week after President Trump unveiled his peace plan for the region.

In separate incidents, an Arab Israeli who shot and wounded an Israeli police officer was killed by police in Jerusalem’s Old City, and Israeli soldiers came under fire from an assailant near the town of Qalqilya in the West Bank.

...