Egyptian and Israeli officials have been warning of a deteriorating security situation in Sinai, where militants have taken advantage of a security vacuum in the area following the uprising that toppled longtime President Hosni Mubarak last year.
The security official said the attack set off clashes with the gunmen. He later said one of the armored vehicles was found abandoned near the border with Israel.
All the Egyptian officials spoke on condition of anonymity because they were not authorized to speak to reporters.
In a statement posted on the website of Gaza's Hamas leaders, Hamas condemned "the ugly crime committed today against the Egyptian soldiers, and sent its condolences to the families of the victims, to Egypt's president and to his government." Hamas did not fix blame for the attack.
The attack caused confusion among the security agencies because of its surprise nature. It took place at a checkpoint near the border where Israel, Gaza and Egypt meet.
Late last week Israel issued one of its frequent warnings to Israelis to leave the Sinai.
Since Mubarak stepped down, Israel has allowed Egypt to send in more troops to Sinai, which has been mostly demilitarized according to the 1979 peace deal between the two countries. The Sunday attack spurred renewed calls in Egypt to amend the treaty to allow for more troops in Sinai.
A similar attack took place last year, when Palestinian militants crossed from Gaza into Egypt's Sinai Peninsula, made their way along the Israel-Egypt border, crossed back into Israel, attacked Israeli vehicles and killed eight people on Aug. 18 last year. Israeli forces killed six Egyptians soldiers as they chased the militants, increasing tension between the two countries.
Relations between the two nations have always been cool. Since Mubarak was overthrown and Islamist parties moved to the front of the Egyptian political scene, Israeli officials have expressed concern about the possibility of deterioration in relations, while insisting that maintaining the peace treaty is in the interest of both countries.
Associated Press writers Daniel Estrin in Jerusalem, Ibrahim Barzak in Gaza City, Gaza Strip and Sarah El Deeb in Cairo contributed to this report.
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