In al-Jalazoun refugee camp, near the de facto Palestinian capital of Ramallah, Palestinians threw rocks at Israeli troops and army gunfire killed a 20-year-old Palestinian and wounded another.
Israel says members of Hamas, which signed a unity deal with Palestinian President Mahmoud Abbas in April, kidnapped the three students who disappeared on Thursday after leaving a Jewish settlement in the occupied West Bank.
Lieutenant-General Benny Gantz, chief of Israel's armed forces, said: "We have a goal, and that is to find these three boys and to hit Hamas as hard as possible. We are on our waytoward a significant campaign. We will get our plans in order."
Prime Minister Benjamin Netanyahu, who broke off peace talks with Mr Abbas after the Palestinian reconciliation pact, held a rare telephone conversation with the Western-backed leader.
In a separate statement, Mr Abbas's office said he condemned the kidnapping.