CAIRO — An obscure militant group based in Egypt’s North Sinai region claimed responsibility over the weekend for a cross-border attack that killed an Israeli soldier last week. The claim called fresh attention to the uphill struggle the newly formed Egyptian government is facing to control the restive Sinai region.

The group, which calls itself Supporters of the Holy Places, said in a statement posted on militant Web sites that it mounted the attack in response to a crude American-made video mocking the Prophet Muhammad, the same video cited in anti-American protests around the Muslim world. The group repeated a false claim that a number of Jews were involved in making the video, an apparent lie initially told by a Coptic Christian, an Egyptian expatriate, who did play a role in the production.

The militant group also said it was responsible for a cross-border attack near the Israeli resort of Eilat last year that killed 8 people and wounded more than 30. The Israeli response to that attack inadvertently killed five Egyptian soldiers, bringing the two nations to the brink of a crisis. The militant group said that one of its leaders, Ibrahim Aweida, helped lead the Eilat attack and that Israel killed him last month in the Sinai village of Khreiza; the attack on Friday was partly to avenge his death, the group said.