An Islamic militant group based in Egypt's Sinai on Sunday claimed responsibility for a cross-border raid, in which one Israeli soldier and three gunmen were killed, media reports said.

Ansar Bayt al-Maqdes, a group of supporters of the holy land in reference to Jerusalem, posted its statement claiming the responsibility on a website used by radical Islamist groups, saying the attack was a response to a U.S.-made anti-Islam movie.

On Friday, a group of gunmen crossed from Egypt's Sinai Peninsula into Israel and ambushed an Israeli patrol guarding workers building a fence along the border.

In the raid, an Israeli soldier was killed and another was injured when one of the assailants detonated himself, and three gunmen were shot dead after another patrol rushed over to rescue their fellow soldiers.

Ansar Bayt al-Maqdes said in the statement that the operation was an attack against those who are against Muslims' Prophet Mohammed. Israel is often viewed by Arabs as the United States' proxy in the Middle East.

The movie "Innocence of Muslims," made in the United States, offended Muslims for denigrating the prophet and triggered angry protests against U.S. diplomatic missions across the Muslim world.