Speaking to President Husni Mubarak by telephone on Thursday, Sharon said no soldier would ever intend to fire into Egypt.
Aljazeera's correspondent, Walid al-Umari, reported that Israel has accepted that an Israeli tank fired a shell into Egypt, and accordingly has begun an investigation.
Israeli Deputy Defence Minister Zeev Boim called it a "regretful incident with terrible results" on Israel Radio but qualified his remarks later in the interview.
"We must remember the area in which the incident took place, the border area between us and Egypt ... is a very tense area and is constantly subject to fighting," Boim said.
Egypt reacted by condemning and strongly protesting against the incident, calling it an "irresponsible" act along the Gaza-Egypt border.
Aljazeera's correspondent in Cairo said the Egyptian army had confirmed that three members of a six-member border patrol died when a tank shell was fired at 3:15am (0115 GMT).
Husain Abd al-Ghani said the tank was less than 20 metres away from the patrol when it opened fire and that all six men were in Egyptian army uniform.
Egyptians accuse Israel of using
harsh tactics against Palestinians
"The Egyptian foreign ministry has demanded an explanation and underlined the fact that the incident represents a grave violation of Egyptian-Israeli peace agreements," he said.
But Eitan Arusi, an Israeli occupation army spokesman, told Aljazeera that the tank shell had been aimed at a "three-member Palestinian cell" but it "unfortunately missed".
"The Egyptian-Israeli borderline is a very narrow and small route. There is a distance of only 10 meters between the two sides," he said.
He also confirmed that an investigation had already begun.
Surge in mishaps
The border incident occurred just hours after the Israeli army, citing a surge in deadly operational mishaps, had scheduled a two-hour break in all training later on Thursday to discuss ways to prevent accidents and reduce negligence in soldiers' performance.
Egypt is one of only two Arab states to have a peace treaty with Israel, the other being Jordan.
Relations between the two countries have been chilly since the outbreak of the al-Aqsa intifada in September 2000, with Egypt accusing Israel of heavy-handed military tactics in the occupied West Bank and Gaza.
Cairo has recently indicated a willingness to help the Palestinian Authority maintain order in Gaza once Israel carries out a unilateral plan to withdraw troops and vacate all illegal settlements from the coastal territory by the end of 2005.