Kasaesbeh was captured after his jet crashed in northeastern Syria in December during a bombing mission against Islamic State, which has captured large tracts of Syria and Iraq.
The voice on the video said Kasaesbeh had a shorter time to live than Goto. Japan confirmed the existence of the video at 11 p.m. (1400 GMT) on Tuesday.
"Twenty-four hours have passed since we confirmed the image of Mr. Goto, but there hasn't been any information of any particular big movement," Japanese Foreign Minister Fumio Kishida told reporters.
He said Japan would continue to do its best to secure his release, staying in contact with Jordan.
Momani said Jordan's priority was to secure the release of the pilot, who hails from an important Jordanian tribe that forms the backbone of support for the Hashemite monarchy.
Several hundred people, including Kasaesbeh's relatives, gathered in front of the office of Jordan's prime minister on Tuesday, urging authorities to meet Islamic State's demands.
Al-Rishawi has been held in Jordan over her role in a suicide bombing that killed 60 people in the capital Amman.
When it comes to Africa, China's inroads are just getting started