Egyptian police said that the two dead men were Egyptian security personnel who, together with a third security officer, exchanged fire with the Israeli soldiers after crossing the border.
The reason for their infiltration into Israel was not immediately clear, said Essam el-Sheik, the head of Egyptian police in the border area.
The Israeli army said three gunmen had entered Israel a few dozen meters (yards) and fired at Israeli troops. When the Israeli soldiers responded, two of the men were killed, the army said. The third man fled, apparently crossing the border into Egypt, the army said.
The incident happened in the central part of the border with Egypt, near Mount Sagi, the army said. Israel Radio said the exchange of fire occured in an area of the border that is not fenced.
The incident came two days before Israeli Prime Minister Ehud Olmert is slated to meet with Egyptian President Hosni Mubarak in the Egyptian resort of Sharm el-Sheik.
The Israeli-Egyptian border is usually quiet except for occasional drug smuggling into Israel. Israel and Egypt signed a peace treaty in 1979, the AP reports.
Biden built a near-half century political career on a foundation of Big Lies and mass deception. They'll surely continue as long as he remains in office.