Self-styled Islamic State militants have released a video appearing to show a captured Jordanian pilot being burnt alive, as Jordan vowed to avenge his death with an "earth-shaking" response.

A Jordanian official said the authorities would execute several militants jailed in Jordan in response, including a Iraqi woman who Amman had sought to swap for the pilot taken captive after his plane crashed in Syria in December.

Jordanian state television said that he had been killed a month ago, on 3 January.

Reuters could not immediately confirm the content of the video, which showed a man resembling airman Mouath al-Kasaesbeh standing in a black cage before being set ablaze.

But the reaction of the Jordanian authorities made clear they treated it as genuine.

The White House said the intelligence community was studying when the video was recorded and that President Barack Obama had ordered his team to devote all resources to locate other hostages held by Islamic State.

Jordan, which has been mounting air raids in Syria as part of the US-led alliance against Islamic State insurgents, would deliver a "strong, earth-shaking and decisive" response.

"The revenge will be as big as the calamity that has hit Jordan," army spokesman Colonel Mamdouh al Ameri said in a televised statement confirming the death of the pilot, who was seized by Islamic State in December.

The fate of Mr Kasaesbeh, a member of a large tribe that forms the backbone of support for the Hashemite monarchy, has gripped Jordan for weeks and provoked rare protests against King Abdullah over the government's handling of the crisis.

Anwar Tarawneh, the wife of Jordanian pilot Muath al-Kasaesbeh, sheds a tear during a rally earlier today calling for his release 

The king cut short a visit to the United States to return home following word of Kasaesbeh's death.

In a televised statement, he said the pilot's killing was an act of "cowardly terror" by a deviant group that has no relation to Islam.

Jordan had sought to swap the pilot for Sajida al-Rishawi, the Iraqi woman militant who was sentenced to death for her role in a 2005 suicide bombing in Amman that killed 60 people.

Islamic State had demanded her release in exchange for the life of Japanese hostage Kenji Goto. The beheading of Goto, a veteran war reporter, was shown in a video released by the group on Saturday.

The Jordanian security source said Rishawi would now be executed "within hours".

The Jordanian military might also escalate attacks on Islamic State, said retired air force General Mamoun Abu Nowar.

"We might even see in a couple of days the rate of sorties increased dramatically. We might have some special operations against their leadership too," he said.

In the Islamic State video, Mr Kasaesbeh is interviewed, describing the mission he was due to carry out before his jet crashed. The video also showed footage of the aftermath of air strikes, with people trying to remove civilians from debris.

A man resembling Mr Kasaesbeh is shown inside the cage with his clothes dampened, apparently with flammable liquid, and one of the masked fighters holds a torch, setting alight a line of fuel which leads into the cage.

The man is set ablaze and kneels to the ground.