Shinzo Abe said on NHK-TV early Sunday that the video is likely authentic and offered condolences to the family and friends of Haruna Yukawa, a 42-year-old adventurer taken hostage last year.
Abe declined to comment on the message on the latest video demanding a prisoner exchange for journalist Kenji Goto.
He had said in an earlier statement that Japan will not give in to terrorism. He called the murder "an outrageous and unacceptable act of violence."
ISIS is demanding the release of a failed female suicide-bomber held in Jordan, in exchange for the remaining Japanese captive.
Sajida Al-Rishawi was arrested after her bombing device failed, in a string of deadly hotel attacks in Jordan ten years ago.
President Barack Obama condemned what he called "the brutal murder" of Yukawa, saying he stood by Japan to get Goto released.