Israel and the United States worked intensively over the weekend to defuse the gravest crisis in Israel-Egypt relations for over a decade, brought on by Thursday's terror attacks on the Egyptian border near Eilat.

Cairo demanded that Israel apologize for killing at least three Egyptian policemen during exchanges of fire with the terrorists, and threatened to recall the Egyptian ambassador from Israel.

Only intensive diplomatic efforts by the Foreign Ministry, Defense Ministry and U.S. officials was able to relieve the strain.

Senior officials at the Foreign Ministry said yesterday that Israel wanted to use the crisis and Thursday's terror attacks as an opportunity to turn over a new leaf with the Egyptian government, and to work together to deal with the deteriorating security situation in Sinai.

Tension with Egypt began to mount Friday afternoon, when reports were released in Cairo that a complaint had been lodged with Israel over the killing of three Egyptian policemen. Egyptian officials said the policemen were killed by Israel Defense Forces soldiers and that Israel should both apologize and launch an investigation.

The Egyptians also demanded an apology for statements by senior Israeli officials, including Defense Minister Ehud Barak, that Egyptian control over Sinai was unraveling.

On Friday evening, the Egyptian cabinet held an emergency meeting, again demanding an apology. Various other statements indicated that Egypt was planning on recalling its ambassador to Israel, Yasser Reda. The last time Egypt recalled its ambassador was 11 years ago, during the second intifada.

Intense diplomatic efforts began Saturday morning to try to end the crisis and prevent Reda's recall. Foreign Minister director general Rafi Barak, the head of the diplomatic-security bureau in the Defense Ministry, Amos Gilad, and National Security Adviser Ya'akov Amidror, all spoke with senior U.S. and French officials. They also spoke directly with officials on Egypt's Supreme Military Council and with Egyptian intelligence officials.

Ehud Barak also apparently spoke yesterday with the head of the Supreme Military Council, Mohammed Hussein Tantawi.

The Israeli officials learned that the statement about recalling the ambassador was made by the cabinet without the approval of the Supreme Military Council.

After consultations in Israel, the Foreign Ministry recommended that Israel issue a statement expressing its regret over the deaths of the Egyptians, without taking responsibility. It was decided that the statement would also express Israel's appreciation for Egypt's willingness to conduct a joint investigation of Thursday's events on the border.

"Israel regrets the deaths of the Egyptian policemen during the attack on the Israel-Egypt border," Ehud Barak said yesterday. Barak also noted the importance of the Israel-Egypt peace agreement and expressed appreciation for the "discretion and responsibility" shown by Egypt.

"The peace agreement between Israel and Egypt is of great importance and strategic value to stability in the Middle East," Barak added. Immediately after Barak released the statement, Israel's temporary head of mission in Cairo, Shalom Cohen, personally took it to the Egyptian Foreign Ministry. Senior Egyptian Foreign Ministry officials lodged a protest over the deaths of the policemen, but said recalling the Egyptian ambassador was not on the agenda.

The IDF said yesterday that soldiers had fired "toward the sources of fire" and had not aimed at Egyptian soldiers. However, the IDF did not rule out the possibility that Egyptian soldiers were hit by IDF fire because terrorists had fired from positions near those of the Egyptian army.

The IDF said Egyptian soldiers were also injured by the explosive charges carried by the suicide bomber who blew himself up near them, and that the terrorists had laid explosives on the Egyptian side of the border as well, which may have injured the Egyptians when they exploded.