CBS News correspondent Robert Berger reports the killing is the latest sign that anbetween Palestinian militants and Israel that had briefly kept the peace, may disintegrate.
The military said the troops were trying to arrest a high-ranking militant in the village and opened fire only when the man refused to surrender and began shooting at them.
Abdel Karim Hammad, whose family lives in the house, said troops surrounded a house in the village of Saida and demanded that its occupants come out.
Saleh Karkur, 27, a wanted Islamic Jihad gunman who was staying with the family, refused to come out and a gunfight erupted and Karkur was shot and killed, Hammad said.
The Israelis then demolished half of the house and arrested Hammad's father for harboring a wanted militant, he said.
AP Television News footage showed the man's body lying atop the ruins of the house. Palestinian medics said they took the body from the scene.
Berger says Islamic Jihad, which frequently fires rockets at Israel, was quick to promise revenge. Palestinian groups have long demanded that any truce include a halt to Israeli raids in the West Bank.
Israel is holding peace talks with the moderate Palestinian government of President Mahmoud Abbas, based in the West Bank. But Israel says the Palestinians are not yet capable of controlling militants in their territory and continues military operations against gunmen.
On Tuesday, a Palestinian rocket fell near the Israeli city of Ashkelon. The Popular Front for the Liberation of Palestine, a tiny militant group, claimed responsibility for the rocket, which Israel said landed in an open area south of Ashkelon, causing no injuries.
Israeli defense officials said the army would not retaliate for the attack, since Hamas militants had not launched the rocket. They spoke on condition of anonymity due to the sensitive nature of the subject.
In Gaza, Islamic Jihad released a statement Wednesday saying Karkur was one of the group's top West Bank commanders and threatened to avenge his death.
Meanwhile, Berger says there are fears in Israel that some Jews may try to seek revenge on Palestinians in Jerusalem for alast week which left eight students dead at a prominent Jewish seminary.
Israel Television reports students at the seminary, which was attacked last Thursday by a Palestinian gunman, are planning to take revenge. The target, according to the reports, would be a senior Palestinian official at the al Aqsa Mosque, the volatile site called the Temple Mount by Jews.
An attack at the mosque could prompt a outbreak of violence across Israel and the Palestinian territories, says Berger. Israeli police say they have prepared for the possibility of a revenge attack, but so far there have been no arrests.