An injured Israeli soldier is wheeled into Soroka hospital in the southern town of Beersheva, Israel, Friday, Sept 21, 2012, following an exchange of fire with militants along Israel's southern border with Egypt. (Yehuda Lahiyani/AP)

An Islamist militant group based in Egypt’s Sinai peninsula has claimed responsibility for a cross-border attack in which an Israeli soldier was killed, calling the raid a response to an online video mocking the prophet Muhammad that triggered protests across the Muslim world.

Three gunmen also were killed in Friday’s firefight on the Israeli-Egyptian border. The incident was the latest in a number of militant attacks from Sinai that have heightened concerns in Israel about what officials say is growing activity by al-Qaeda-inspired jihadist groups in the desert region since the Egyptian revolution last year.

In a statement posted on militant Internet forums late Saturday, a group calling itself Ansar Bait al-Maqdis, or Partisans of Jerusalem, called the deadly raid a “disciplinary attack against those who insulted the beloved Prophet,” referring to the controversial anti-Islam YouTube video “Innocence of Muslims.”

The group alleged that Jews were involved in the video, though it was produced in the United States and has been linked to an Egyptian-born Coptic Christian living in California. Initial reports had said the video was made by an American Israeli with Jewish financial backing.

Ansar Bait al-Maqdis said three militants had infiltrated into Israel early Thursday and remained in hiding until midday Friday when they spotted and fired on an Israeli patrol.

The group pledged to carry out another attack to avenge what it said was Israel’s role in the killing of one of its fighters, Ibrahim Aweida, who died in a blast in Sinai last month. According to the group, Aweida led a cross-border attack in August 2011 that left eight Israelis dead on a road north of the Red Sea resort of Eilat.

Jihadist groups have posted videos claiming responsibility after previous attacks from Sinai into Israel. Ansar Bait al-Maqdis said it was behind the firing of two rockets last month at Eilat, and an earlier attack on a pipeline carrying natural gas to Israel.

Egyptian forces using armored vehicles and helicopters launched a crackdown on militants in Sinai after an assault last month on an Egyptian base that killed 16 border guards near the town of Rafah.

There have been calls in Egypt to revise the security annex to the 1979 peace treaty with Israel to allow higher troop levels in the area to combat the militant threat and assert control. The treaty limits the size and armaments of Egyptian forces in Sinai.

Israel has agreed to the dispatch of some additional Egyptian forces to the area, but Israeli Foreign Minister Avigdor Lieberman, an outspoken hawk, on Sunday ruled out any change in the treaty.

“There’s no chance that Israel will agree to any kind of change” in the pact, Lieberman told Israel Radio. “The problem in Sinai is not the size of the forces, it is their readiness to fight, to put pressure and to carry out the job as needed.”