Israel moved swiftly to contain an escalating crisis with its ally Egypt following Thursday's cross-border attack by militants in which at least three Egyptian policemen were killed. Defence minister Ehud Barak was forced to apologise for the deaths after Egypt said it would withdraw its ambassador to Israel as tensions between the two countries rose sharply.

The fallout from the attack continued to spiral on Saturday, both in terms of a diplomatic breach with Israel's strategically vital neighbour and continued exchanges of rocket and missile fire between Gaza and Israel.

Egypt demanded an apology for Israel's "hasty and regrettable statements" about the security situation in the Sinai, from where Thursday's attack was launched. Following the attack, Israel's defence minister Ehud Barak spoke of "the weakening Egyptian grip on Sinai and the widening operation of terrorists there" and Israeli officials briefed that Egypt's had lost control of the area.

Egypt also demanded an investigation into the deaths of its policemen, who were killed when Israeli forces chased the militants across the border.

Barak issued a statement, saying "Israel is sorry over the deaths of the Egyptian officers". He launched a military investigation and a joint inquiry with the Egyptian army.

The incident unleashed a wave of anti-Israel feeling in Cairo. Protesters gathered outside the Israeli embassy following Friday prayers, waving Palestinian flags and chanting "Death to Israel".

Amr Moussa, the former head of Arab League and a Egyptian presidential candidate, said: "Israel and any other [country] must understand that the day our sons get killed without a strong and appropriate response is gone and will not come back."

In a statement, the Egyptian government said: "The cabinet committee has decided to withdraw the Egyptian ambassador in Israel until the result of investigations by the Israeli authorities is provided and an apology from the Israeli leadership over the hasty and regrettable statements about Egypt is given.

"Egypt deplores the irresponsible and hasty statements made by some leaders in Israel, which lack wisdom and prudence and passes judgment before arriving at the truth, particularly keeping in mind the sensitivity of Egyptian-Israeli relations."

Israeli officials insisted the two countries were co-operating in the aftermath of Thursday's attack. "At an army and defence ministry level we are working together. It's in our mutual interests," said one.

Since the fall of the Mubarak regime in February, Israel has been worried about the future of its relations with one of the only two Arab countries with whom it has signed a peace treaty. Mubarak was considered a friend of Israel and kept the Islamist Muslim Brotherhood, which has strong connections to Hamas in Gaza, in check.

Israel fears that the post-Mubarak regime will be more sympathetic to Hamas and could even revoke the 1979 peace treaty with Israel. "They feel the need to respond to the [Arab] street," said an Israeli government official. "Instead of calming things down, they are being dragged." The Egyptian statement was "a very dismal development", he said.

Israel blamed Thursday's attacks on Palestinian militants who it said had entered Egypt through tunnels from Gaza, travelled around 200km through the Sinai and entered Israel about 20km north of Eilat. Six Israeli civilians, two Israeli soldiers and seven militants were killed in gun fire and explosions.

A senior Israeli military officer said it was possible that some Egyptians may have been killed accidentally by Israeli fire during the fighting. "It is a possibility that it happened by mistake," he said. Some of the attackers might have been wearing Egyptian army or police uniforms, he added.

Egyptian officials suggested their policemen were killed in gunfire from an Israeli helicopter which was pursuing militants across the border.

Israeli concern about security in the Sinai, a vast area of desert mainly inhabited by Bedouin, has been growing since the fall of Mubarak. They claim claim the Egyptian government has lost control of the area, which has become a haven for terrorists and criminals. A vital gas pipeline, which supplies Israel, has been sabotaged several times in recent months.

The cycle of rocket fire from Gaza and Israeli airstrikes continued today. According to the IDF, at least six rockets landed in southern Israel during the morning, with one seriously injuring three Palestinians who were working illegally in the city of Ashdod. Around 30 rockets were fired on Friday.

Israeli warplanes continued to target sites in Gaza, killing three people overnight. Three children aged 2, 5 and 13 are among the 15 people killed in airstrikes since Thursday, according to Palestinian sources.

Hamas's military wing said it was calling off a truce with Israel in place since early 2009. However, a Hamas political spokesman denied this had been agreed. The Hamas leader in Gaza, Ismail Haniyeh, called on Egypt and the United Nations to intervene "to stop the aggression on Gaza".

The Gaza-based Popular Resistance Committee, which Israel claims was behind Thursday's attack, denied involvement but said its militants had fired rockets on Friday. Israeli airstrikes have killed at least five leaders of the PRC in the past two days.

Israel's relations with another regional ally, Turkey, are also fragile following its refusal to apologise for the deaths of nine Turkish citizens on board the Mavi Marmara, part of the flotilla of ships attempting to take aid to Gaza, last year.