Defense Minister Ehud Barak said on Saturday that Israel regrets the deaths of three Egyptian policemen who were killed on Thursday.

IDF soldiers fired across the Israel-Egypt border as they intercepted the terrorist cell behind the attacks near Eilat in which eight Israelis were killed. Egypt has blamed Israel for deaths.

The deaths of the Egyptian policemen fueled a demand from Egypt for an apology and gave rise to a report that Egypt was to recall its ambassador to Israel, which was later denied by the Egyptian government.

"Israel regrets the deaths of the Egyptian policemen during the attack on the Israel-Egypt border," Barak said on Saturday.

Barak ordered the IDF to investigate the incident after which a joint investigation will be conducted with the Egyptian military to determine the circumstances of the incident.

An Egyptian Foreign Ministry official said on Saturday that a verbal apology from Israel would not be enough.

Barak 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 said.

Barak's statement came after he held a special situation assessment with IDF Chief of Staff Benny Gantz and other security and intelligence officials.

"The attacks came from the Gaza Strip," Barak said. "Most of the perpetrators were killed and the officials responsible for sending them were eliminated shortly after the attacks.The IDF has been striking hard over the past two days against those reponsible for [Thursday's] attacks in the south and is operating efficiently against rocket launchers in Gaza in order to protect Israel's citizens."

The most senior echelons of the Israeli government met Saturday morning to discuss ways to halt further deterioration in the country's ties with Egypt, following Thursday terror attacks.

An official statement was issued following the Saturday morning discussions involving Barak, Prime Minister Benjamin Netanyahu and Foreign Minister Avigdor Lieberman.

According to a senior Israeli source, the statement said that "the main aim is to halt deterioration [in bilateral ties] and prevent the departure of the Egyptian ambassador."