Frank Gardner reports on Moaz al-Kasasbeh's death
Jordan has confirmed the death of pilot Moaz al-Kasasbeh after a video published online by Islamic State (IS) claimed to show him being burned alive.
The video shows a man standing in a cage engulfed in flames. Officials are working to confirm its authenticity.
Jordan's King Abdullah hailed Lt Kasasbeh as a hero, saying Jordan must "stand united" in the face of hardship.
The pilot was captured when his plane came down near Raqqa, Syria, during a mission against IS in December.
The video posted on Tuesday was distributed via a Twitter account known as a source for IS propaganda.
The highly produced 22-minute film includes a sequence showing the Jordanian pilot walking at gunpoint amongst rubble apparently caused by coalition air strikes that targeted jihadists.
BBC security correspondent Frank Gardner says that in a world already shocked by the calculated cruelty of Islamic State's actions, the horrific video is aimed primarily at Arab populations in Jordan and the Gulf states.
Jordanian state TV reports that Lt Kasasbeh, 26, was killed a month ago. Jordan had tried to secure his release since then.
The country has vowed "punishment and revenge" for his death, and the king described IS as a "deviant criminal group".
Jordan, which has joined the US-led coalition against IS, had been attempting to secure Lt Kasasbeh's release as part of a prisoner swap, offering to free Iraqi militant Sajida al-Rishawi in exchange.
She is a failed suicide bomber now on death row in Jordan for her role in attacks in the capital, Amman, that killed 60 people in 2005.
IS had sought Rishawi's release as part of a deal to free captive Japanese journalist Kenji Goto. A video that appeared to show Goto's dead body appeared three days ago.
At the scene: Paul Adams, BBC News, Amman
Relatives had gathered around Lt Kasasbeh's father (centre) in Amman
Jordanians greeted the news with horror. Many have seen the gruesome video, barely edited, played over and over on television.
Hundreds gathered in the streets after dark, demanding revenge against Lt Kasasbeh's killers. Some also wanted to know why Jordan was involved in this fight at all.
The pilot's father was among supporters when the news came through. He and other family members have left the capital to mourn at home.
King Abdullah said Lt Kasasbeh had died defending his beliefs and homeland. The defence ministry said the pilot's blood would not have been shed in vain. It is promising a fitting punishment.
For many Jordanians, this has to begin with the quick execution of Sajida al-Rishawi, the failed al-Qaeda suicide bomber, jailed 10 years ago for her part in a spate of bombings against hotels here.
A spokesman for the Jordanian armed forces, Mamdouh al-Ameri, said Lt Kasasbeh had "fallen as a martyr".
"His blood will not be shed in vain," he said. "Our punishment and revenge will be as huge as the loss of the Jordanians."
Jordanian officials were quoted as saying Rishawi would be executed imminently, along with three other convicted militants.
Late on Tuesday, supporters of the pilot expressed their anger at a rally in Amman
Analysis: Jonathan Marcus, BBC diplomatic correspondent
One thing is clear from this video - Islamic State never had any intention of releasing the young Jordanian pilot. According to Jordanian state media he was killed on 3 January, well before the supposed prisoner exchange talks moved into high gear.
The cynical manipulation of this episode by IS shows the importance it affords to information warfare - here an attempt to create problems for the Jordanian authorities and to weaken the Arab-Western coalition, at a time when it appears to be struggling to make dramatic headway against IS on the ground.
This is the problem for the coalition. Its air campaign is in many ways a stop-gap intended to halt the progress of IS, but requiring effective troops on the ground to significantly turn back its advance.
Jordan's King Abdullah is cutting short a visit to the US after news of Lt Kasasbeh's death, but will meet President Barack Obama before he heads home.
Mr Obama earlier said in a statement that if the video was real, it would be "one more indication of the viciousness and barbarity" of IS.
"I think it will redouble the vigilance and determination on the part of the global coalition to make sure they are degraded and ultimately defeated," he added.
The Jordanian king has already met US Vice-President Joe Biden who "reinforced America's ironclad support" for Jordan, the White House said.
Timeline: Jordanian pilot held hostage
24 December 2014: Jordanian Lt Moaz Youssef al-Kasasbeh captured by IS after his plane crashes
25 December 2014: Pilot's father urges IS to show mercy
20 January 2015: IS threatens to kill two Japanese hostages unless Japan pays $200m ransom within 72 hours
24 January: IS releases video of Japanese hostage Kenji Goto holding a picture apparently showing Haruna Yukawa's decapitated body
24 January: IS calls for release of Sajida al-Rishawi, an Iraqi militant sentenced to death in Jordan
28 January: Jordan offers to release Rishawi in exchange for Lt Kasasbeh
29 January: Deadline to kill Lt Kasasbeh and Mr Goto expires
31 January: Video released appearing to show Kenji Goto's body
3 February: Video released appearing to show Lt Kasasbeh burnt alive, with Jordanian media suggesting he was killed weeks earlier