TOKYO — As the shock from the beheadings of two Japanese hostages by the Islamic State faded Tuesday, a battle to gain political advantage from their deaths began.

Prime Minister Shinzo Abe called for the unshackling of Japan’s military, while the opposition accused him of having provoked the crisis.

The political maneuvering came as the Islamic State caused new revulsion, posting a video of a captive Jordanian pilot being burned to death.

Speaking in Parliament, Mr. Abe said that he wanted to ease the tight legal restrictions currently placed on Japan’s purely defensive military to allow it to engage in what he called police actions overseas, such as freeing hostages.