TEL AVIV—A Palestinian gunman killed two Israeli soldiers in the occupied West Bank, Israel’s military said, the latest bloodshed in a spurt of violence that authorities here have struggled to control or explain.

The soldiers were gunned down east of Ramallah on Thursday after Israel’s killing this week of two Palestinian suspects in separate high-profile shootings of Israelis in the West Bank. Israel’s military sent additional forces to the West Bank and put up roadblocks around Ramallah to search for the soldiers’ killer.