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(CNN) -- A radical group inspired by al Qaeda has claimed responsibility for a deadly attack along the Egyptian-Israeli border.
In a statement posted on jihadi websites late Saturday, a group calling itself Ansar Jerusalem ("Supporters of Jerusalem") said the Friday attack, in which three militants and an Israeli soldier were killed, was a response to the anti-Islam film "Innocence of Muslims."
The statement claimed that the militants were Egyptians and that the operation was a "disciplinary attack against those who insulted the beloved Prophet" Mohammed.
General Ahmed Bakr, head of North Sinai security, said, "There is no evidence of highly organized groups in Sinai regardless of such statements released on the net."
There are dozens of "groups of armed militants who have been weakened by our military operation in Sinai, and sooner or later will be demolished completely," he said.
On Saturday, three militants armed with weapons and explosive belts tried to cross into Israel and were targeted by troops, an Israeli military statement said.
One soldier was killed in the exchange of fire and another was wounded, and the three militants were killed, the military said.
"According to initial findings, the IDF force successfully prevented a large-scale attack on Israeli civilians," the statement said.
A senior Egyptian security official said that one of the militants died after detonating his explosive belt, and Israeli forces killed the other two. The official spoke on condition of anonymity because he is not authorized to speak with the media.
None of the attackers was able to slip into Israel, the military said.
Egyptian authorities believe the militants were known jihadists and members of the same Bedouin tribe who were wanted by Sinai police, the official said.
In its statement, the group said three militants had crossed the border into Israel early Thursday and remained in hiding until Friday, when they attacked an Israeli patrol protecting civilians who were building a fence on the Israeli side designed to stop infiltrators from entering the country,.
The statement also accused Israel of the August 26 killing of Ibrahim Aweida, one of its leaders, in the Sinai village of Khreiza, 15 kilometers (10 miles) from the Israeli border.
Aweida was killed by a mysterious explosion while driving his motorcycle and was later identified by Israel as a long time jihadi with alleged involvement in an August 2011 attack on an Israeli bus in Eilat that killed six people. Egyptian authorities at the time said he may have been killed by an Israeli drone.
Bakr said Egypt, under new President Mohamed Morsy, is "determined" to cleanse Sinai of all criminal and jihadi pockets.
"This is a work of local militants who are trying to spark sedition between Israel and Egypt and have capitalized on the tragic video to further justify their cause and appeal to the emotions of other Islamists," he said.
The anti-Islam video, on YouTube, has angered Muslims around the world and helped spark protests, and in some cases violence, at U.S. facilities including the U.S. Consulate in Benghazi, Libya, where U.S. Ambassador Chris Stevens and three other Americans died.
Jihadi Movements in Sinai recently released a statement denouncing attacks on the Egyptian military and saying their enemy Is Israel. That statement claimed responsibility for repeatedly bombing a pipeline that carries gas to Israel, as well as rocket attacks on Eilat.
Morsy appointed a group of former jihdists, including Mohamed Al Zawahiri, the brother of al Qaeda leader Ayman Al Zawahiri, and sent them to Sinai to negotiate a truce with operational jihadists in the Sinai.
The Egyptian military has announced shutting down dozens of tunnels used to smuggle militants from Gaza into the Sinai. Egypt announced in a recent statement that the military had killed 32 suspected terrorists and shut down 31 tunnels.