"We have been looking into its authenticity, but unfortunately at the moment we cannot help saying its credibility is high," he said on the public network NHK.
"Considering the unbearable pain and sorrow that his family must be feeling, I am speechless," he said.
"Such act of terrorism is outrageous and impermissible, it causes me nothing but strong indignation," he added. "I condemn it strongly and resolutely."
The government will continue analysing the images to fully confirm the authenticity of the video, Abe said.
It was not posted on any of the group's official channels and it does not bear their black and white flag. The purported execution of Yukawa is also not shown.