An Islamist militant group based in Egypt's Sinai has claimed responsibility for a cross-border attack that killed an Israeli soldier in the restive peninsula where jihadi groups have gained a foothold.

Three gunmen were also killed in Friday's attack, which the group Ansar Bayt al-Maqdes said was in response to an anti-Islam film that has sparked worldwide protests and violence. A second Israeli soldier was wounded in the attack.

There have been at least four such cross-border raids in just over a year in the area where security lapsed after the overthrow of former President Hosni Mubarak last year.

Egypt's army and police launched a security sweep after a raid that killed 16 Egyptian border guards in August.

In a statement on an Internet site often used by jihadi groups, Ansar Bayt al-Maqdes said it had named the operation as an "attack to discipline those insulting the beloved Prophet", a reference to the film that mocked Prophet Mohammad.

The group accused Jews of involvement in the film, but did not explain how. Though the film was made in the United States, Israel is often viewed by militants as a proxy agent for US policy in the region because it is a close ally of Washington.

CNN reported that Jewish groups denied some reported allegations that there was any Jewish backing for the film.

The US government has condemned the film and said it had no role in it, but said it could not act against the production because of its commitment to freedom of expression.

Many Muslims view any portrayal of the Prophet as blasphemous.

Ansar Bayt al-Maqdes, which means "supporters of the holy place," a reference to Jerusalem, pledged to carry out another operation, at an unspecified time, in revenge for what it said was the killing of a member in Sinai with the help of Israel.

It was not immediately clear what help it believed Israel had given in the death of Ibrahim Oweidah. Egyptian authorities had said his death in September was due to a landmine accident.

The group has previously claimed an attack on a pipeline delivering gas to Israel and rocket attacks targeting Israel.