U.S. President Barack Obama said that the video, if real, would serve only to redouble the determination of the U.S.-led alliance to degrade and destroy ISIL. He added it would be another sign of the "viciousness and barbarity" of the group.
"Whatever ideology they're operating off of, it's bankrupt," he told reporters.
ISIL controls swaths of Syria and Iraq, and it had demanded the release of Sajida al-Rishawi — a would-be suicide bomber convicted and serving a prison sentence over a 2005 attack in Amman, Jordan — in exchange for Kassasbeh's life.
Jordan's government had said it was willing to trade Rishawi but wanted proof that Kassasbeh was alive first.
The latest video emerged three days after Japanese journalist Kenji Goto was purportedly beheaded by ISIL fighters. The fate of the two captives had been linked, but a video of Goto's apparent slaying released Saturday made no mention of the pilot.
An audio message last week, also said to be from ISIL, said only that Kassasbeh would be killed if Rishawi was not released by Thursday, without actually proposing a swap.
A scroll on Jordan TV on Tuesday said that Kassasbeh was killed on Jan. 3, raising questions over whether any of the hostage negotiations were sincere.
Al Jazeera and wire services