The footage was released after a 72-hour deadline imposed by the jihadists passed, with Japan refusing to pay the $200 million ransom for the hostages.
SITE reported that the message was sent to Jogo's family and the Japanese government. In the video, Jogo relays the Islamic State group's latest demand.
The video contains a still image of Jogo holding what appears to be a picture of the beheaded hostage, Haruna Yukawa. According to Reuters, the Japanese government is currently authenticating the footage.
In the footage, Jogo tells the Japanese government they must secure the release of Sajida al-Rishawi, a convicted al-Qaeda terrorist, from Jordan in order to save his life.
Chief Cabinet Secretary Yoshihide Suga said the apparent execution was "outrageous" and "unacceptable" and demanded the release of Kenji Goto.
The US intelligence community was working to verify the authenticity of the recording, according to a senior official.
According to the report, al-Rishawi participated in the 2005 bombing of an Amman hotel that left 38 dead, and has been sentenced to death by hanging after her capture by Jordanian authorities.
One militant on an ISIS-affiliated website warned that Saturday's new message was fake, while another said that the message was intended only to go to the Japanese journalist's family. A third militant on the website noted that the video was not issued by al-Furqan, which is one of the media arms of ISIS and has issued past videos involving hostages and beheadings. Saturday's message did not bear al-Furqan's logo.
The militants on the website post comments using pseudonyms, so their identities could not be independently confirmed by the AP. However, their confusion over the video matched that of Japanese officials and outside observers.
IS released a video on Tuesday demanding $200 million for the release of the hostages and calling on Japan to stop its "foolish" support for the US-led coalition waging a military campaign against Islamic State.
The release of that video coincided with a visit by Japanese Prime Minister Shinzo Abe to Jerusalem, where he said said the ultimatum "is unforgivable and I feel strong resentment."
Reuters and the Associated Press contributed to this report.