The military confirmed the death of Lt. Muath Al-Kaseasbeh, 26, who fell into the hands of the militants in December when his Jordanian F-16 crashed near Raqqa, Syria, the de facto capital of the group's self-styled caliphate. He is the only pilot from the U.S.-led coalition to have been captured to date.
At a tribal meeting place where the pilot's relatives have waited for weeks for word on his fate, chants against Jordan's King Abdullah II erupted and some family members wept. An uncle shouted in Arabic: "I received a phone call from the chief of staff saying God bless his soul."
Hundreds of protesters later took to the streets, chanting: "There is no god but God and the martyr is beloved by God."
The video appeared aimed at pressuring Jordan to leave the coalition that has been battling to roll back the Islamic State group. Jordan's king, a close Western ally, has portrayed the campaign against the extremists as a battle over values, but the airstrikes against fellow Muslims are not popular in Jordan.
The spokesman for the Jordanian armed forces confirmed the death of the "hero pilot" and vowed revenge.
"While the military forces mourn the martyr, they emphasize his blood will not be shed in vain. Our punishment and revenge will be as huge as the loss of the Jordanians," Mamdouh al-Ameri said in a statement read on Jordanian TV.
Following militant demands, Jordan's government had said it was willing to trade Sajida al-Rishawi, an al-Qaida prisoner, for the pilot, but that it wanted proof of life first. Al-Rishawi faces death by hanging in Jordan for her role in triple 2005 hotel bombings that killed 60 people.
The Associated Press was not immediately able to confirm the authenticity of the video, which was released on militant websites and bore the logo of the extremist group's al-Furqan media service. The 20-minute-long video featured the slick production and graphics used in previous Islamic State videos.
The video included purported images of the pilot showing signs of having been beaten, including a black eye. At the end of the video he is purportedly shown wearing an orange jumpsuit and standing in an outdoor cage as a masked militant lights a line of fuel leading to it.
The video threatened other purported Jordanian pilots by name.
The latest video emerged three days after Japanese journalist Kenji Goto was purportedly beheaded by the militants. The fate of the two captives had been linked but a video of Goto's purported slaying released Saturday made no mention of the pilot.
An audio message last week, also purportedly from the Islamic State group, said the pilot would be killed if al-Rishawi was not released Thursday, without actually proposing a swap.
A scroll on Jordan TV said the pilot was killed on Jan. 3, raising questions over whether any of the hostage negotiations were sincere.
U.S. President Barack Obama said if the video is found to be authentic it would be "just one more indication of the viciousness and barbarity of this organization."
"It will redouble the vigilance and determination on the part of the global coalition to make sure that they are degraded and ultimately defeated," he told reporters during an event at the White House.
Obama later issued a statement offering condolences, saying the pilot's "dedication, courage, and service to his country and family represent universal human values that stand in opposition to the cowardice and depravity of ISIL, which has been so broadly rejected around the globe."
The Islamic State extremist group, which controls around a third of Syria and neighboring Iraq, has released a series of grisly videos showing the killing of captives, including two American journalists, an American aid worker and two British aid workers. Tuesday's was the first to show a captive being burned alive.
David L. Phillips, a former State Department adviser on the Middle East, said he believes the brutal killing of the pilot could backfire, antagonizing Sunni Muslims against the Islamic State group, including Sunni tribes in Iraq.
"They need to have a welcome from Sunni Arabs in Anbar Province (in Iraq) to maintain their operations," said Phillips, director of the Program on Peace-building and Human Rights at Columbia University.
He said the extremist group's recent military setbacks may have fueled the killings. "They need to compensate for that with increasingly gruesome killings of prisoners," he said.
In Washington, Jordan's King Abdullah II met privately with members of the Senate Foreign Relations Committee. The panel's chairman, Sen. Bob Corker, R-Tenn., offered condolences to the king at the start of the meeting. Abdullah did not comment when reporters shouted questions as he arrived.
Jordan has made clear that the hostage crisis will not prompt it to leave the U.S.-led military coalition against the Islamic State group.
"We now all know in Jordan, beyond any doubt, how barbaric ISIS is," Jordanian government spokesman Mohammed al-Momani said. "Whoever doubted the unity of Jordan will now be proved wrong. Whoever doubts Jordan's stern and lethal response will be proved wrong."
Experts are divided over whether Jordan faces a greater threat from extremists outside its borders or from those within. In recent months, there have been signs of greater support for the Islamic State group's ideas among Jordan's young and poor. Last year, the government intensified a crackdown on IS sympathizers and the al-Qaida branch in Syria.
Currently, about 220 Jordanians are in prison because of alleged ties to such groups, including 30 who are serving terms from three to five years, said Marwan Shehadeh, an expert on militant groups.
Krauss reported from Cairo. Associated Press writers Karin Laub in Jerusalem, Mohammed Daraghmeh in Ramallah, West Bank, Bassem Mroue in Beirut and Jim Kuhnhenn in Washington contributed to this report.
Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.