The chief of the U.S.-led war on IS, General Lloyd Austin, condemned the pilot's murder as "savage" and vowed to "fight this barbaric enemy until it is defeated".
British Prime Minister David Cameron said the "sickening murder will only strengthen our resolve to defeat ISIL", another acronym for the group.
Kassasbeh was captured on December 24 after his F-16 jet crashed while on a mission over northern Syria as part of the US-led coalition campaign against the jihadists.
The video released Tuesday shows footage of him at a table recounting coalition operations against IS, with flags from the various Western and Arab countries in the alliance projected in the background.
It then shows Kassasbeh dressed in an orange jumpsuit and surrounded by armed and masked IS fighters in camouflage.
It cuts to him standing inside the cage and apparently soaked in petrol before a masked jihadist uses a torch to light a trail of flame that runs to the cage and burns him alive.
The release of the video of the pilot's purported murder came days after IS beheaded a second Japanese hostage within a week.
Shiraz Maher, from the International Centre for the Study of Radicalization at King's College London, described the footage as "simply the most horrific, disgusting thing I have seen from Islamic State in the last two years".
"They clearly want to make a real point. This is the first individual whom they have captured who has been directly involved with the Western coalition in fighting IS. It is different from the aid workers... This is an act of belligerence".
"Every time you think they cannot commit anything worse -- they open up another trapdoor."
IS had vowed to kill the second Japanese, Kenji Goto, and Kassasbeh by sunset on January 29 unless Amman handed over Iraqi jihadist and Rishawi.
Kassasbeh's plane was the first loss of an aircraft since the coalition launched strikes against IS last year.
Along with Jordan, Saudi Arabia, the United Arab Emirates and Bahrain are taking part in the coalition air strikes in Syria. Australia, Belgium, Britain, Canada, Denmark, France and the Netherlands are participating in Iraq.
The extremist group seized swathes of territory in Iraq and Syria last year, declaring an Islamic "caliphate" and committing a wave of atrocities.
IS claimed in a video released Saturday that it had killed 47-year-old Goto, after previously murdering another Japanese hostage, Haruna Yukawa.
The group had initially demanded a $200 million (175 million euro) ransom for the Japanese hostages -- the same amount Tokyo had promised in non-military aid to countries affected by IS.
It had previously beheaded two US journalists, an American aid worker and two British aid workers in similar highly choreographed videos.
Jordan had vowed to do everything it could to save the pilot but had demanded proof he was still alive before handing over Rishawi.
IS had previously published what it said was an interview with the pilot in which he said his plane was hit by a heat-seeking missile.
IS claimed to have shot down his plane but both Jordan and the United States said it had crashed.
Kassasbeh's family had urged IS to release the recently married pilot, with his father Safi asking the jihadist group to show "mercy".
After the killing of Goto, the UN Security Council condemned the "heinous and cowardly" murder, calling for "the immediate, safe and unconditional release of all those who are kept hostage" by the group.
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