A group inspired by Al Qaeda and based in Egypt's Sinai peninsula has claimed responsibility for a shootout along the Israeli-Egyptian border in which three militants and an Israeli soldier were killed.

Ansar Jerusalem, in a statement posted on militant forums late Saturday, linked the attack to an online video denigrating the Prophet Muhammad that has sparked protests across the Muslim world.

It said the militants were Egyptians and that the operation was a "disciplinary attack against those who insulted the beloved Prophet."

The group alleged Jewish involvement in the low-budget film, though it was produced in the United States by an American citizen who is originally from Egypt. It also praised Muslim demonstrations over the film that were directed at U.S. diplomatic facilities in many countries.

Ansar Jerusalem said three militants had crossed the border into Israel early Thursday and remained hiding until midday Friday, when they saw and attacked an Israeli patrol. It accused Israel in the Aug. 26 killing of Ibrahim Aweida, one of its leaders, in the Sinai village of Khreiza, 10 miles from the Israeli border, and warned of more attacks against Israel.

Aweida led an attack last year that killed eight Israelis near Eilat, according to the group.

The Israel-Egypt border has become particularly volatile since the fall of longtime Egyptian ruler Hosni Mubarak in a popular uprising last year. Several militant groups mushroomed in Sinai, staging multiple attacks on a pipeline delivering gas from Egypt to Israel, frequently lobbing rockets into the Jewish state and sneaking across the border and killing Israelis.