JERUSALEM, July 5 (UPI) -- Israeli Defense Minister Ehud Barak has ordered the military to begin demolishing the homes of two men who killed Israelis, officials said.

Barak signed the demolition orders Friday for homes belonging to Ala Abu Dhaim, who was shot to death after he gunned down eight seminarians in March, and for the home of Husam Taysir Dwayat, who was killed after he took the lives of three Israelis in a rampage with a bulldozer Wednesday, The Jerusalem Post reported Saturday.

While Dhaim was a fervently religious Palestinian, his family said he didn't belong to any militant group. Dwayat's was described by family and friends as being a drug-user who had a child with a Jewish woman and had run-ins with police but not as a political extremist.

Israeli Attorney General Menahem Mazuz said Thursday that while the government has the legal right to destroy homes within Israeli sovereignty, doing so could raise "significant legal problems."

Israeli Prime Minister Ehud Olmert has called for more severe punishment of Israeli citizens involved in terror attacks.

"If we need to demolish houses, we'll demolish houses, and if we need to revoke benefits, we'll do that," he said at the Israeli Democracy Institute's Caesarea conference in Eilat.