AMMAN (Reuters) - Jordan has executed by hanging a jailed Iraqi woman militant whose release had been demanded by the Islamic State in Iraq and Syria (ISIS) that burnt a captured Jordanian pilot to death, a security source said on Wednesday.

Responding to the killing of the pilot, whose death was announced late on Tuesday, the Jordanian authorities also executed another senior Al-Qaeda prisoner sentenced to death for plots to wage attacks against the pro-Western kingdom in the last decade.

Sajida al-Rishawi, the Iraqi woman militant, was sentenced to death for her role in a 2005 suicide bomb attack that killed 60 people. Ziyad Karboli, an Iraqi Al-Qaeda operative, who was convicted in 2008 for killing a Jordanian, was also executed at dawn, the source said.

The prisoners were executed in Swaqa prison, a large facility 70km south of the capital, Amman, just before dawn, a security source who was familiar with the case said. "They were both calm and showed no emotions and just prayed," the source added, without elaborating.

Rishawi, in her mid-forties, was sentenced to death for her role in a 2005 suicide bomb attack that killed 60 people. It was the worst Islamist suicide attack in Jordan's history.

Jordan, which has been mounting air raids in Syria as part of the US-led alliance against ISIS insurgents, said it would deliver a "strong, earth-shaking and decisive" response to the killing of pilot Mouath al-Kasaesbeh. "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 ISIS in December.

Scores of Jordanians, infuriated by First Lieutenant Kasaesbeh's killing, gathered at midnight in a main square in the capital calling for revenge and her quick execution.

Holding placards showing images of the pilot, several youths chanted "Death, Death to Daesh", using a pejorative Arabic acronym for ISIS.

The fate of Lt Kasaesbeh, a member of a large tribe that forms the backbone of support for the country's Hashemite monarchy, has gripped Jordan for weeks and some Jordanians have criticised King Abdullah for embroiling them in the US-led war that they say will provoke a militant backlash.

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 had no relation to Islam.

ISIS militants released a video on Tuesday appearing to show a captured Jordanian pilot being burnt alive in a cage. On Sunday, ISIS militants said they had beheaded a second Japanese man they had been holding hostage.

A Jordanian official had earlier said that the authorities would swiftly execute several militants in retaliation, including an Iraqi woman whom Amman had sought to swap for the pilot taken captive after his plane crashed in Syria in December.

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

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

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

ISIS had demanded her release in exchange for the life of Japanese hostage Kenji Goto. However, Mr Goto, a veteran war reporter, was later beheaded by the group, with images of his death released in a video on Saturday.

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

The Jordanian military might also escalate attacks on ISIS, 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 ISIS video, Lt 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 Lt 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.

Fighters then pour debris, including broken masonry, over the cage which a bulldozer subsequently flattens, with the body still inside. The video shows a desert setting similar to previous videos of killings.

In the pilot's hometown of Karak in southern Jordan, people demanded revenge. "I want to see Sajida's body burnt and all the other terrorists in Jordanian prisons ... Only then will my thirst for revenge be satisfied," said Mr Abdullah al-Majali, a government employee among dozens of demonstrators in the centre of Karak.

Relatives of the pilot also gathered in Karak and urged calm after anti-government protests broke out in the town. They said it was up to the government to take revenge for them.

Jordanian state television said on Tuesday that Lt Kasaesbeh had been killed a month ago, on Jan 3, and a source close to the Jordanian government said Amman had been picking up intelligence for weeks that the pilot was killed some time ago.

Given that Jordan's own intelligence indicated the pilot was dead, the government decided it could not possibly release the woman absent convincing proof the pilot was still alive, the source said, and such proof never arrived.

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

Mr Obama rearranged his schedule on Tuesday to make sure he saw King Abdullah before the Jordanian leader flew back to Amman, a source familiar with the situation said.

A staunch US ally, Jordan is part of the alliance against the ISIS that has seized large areas of Syria and Iraq. King Abdullah has defended the campaign against domestic criticism, saying that moderate Muslims need to combat a group whose ideology and brutality have insulted Islam.

The United States announced on Tuesday that it will increase annual aid to Jordan to US$1 billion (S$1.34 billion) from US$660 million to help it pay for the cost of housing refugees from Iraq and Syria and to fight ISIS.

Mr Obama praised Lt Kasaesbeh for his bravery and said he was "in the vanguard of the effort to degrade and defeat the threat"posed by militants from ISIS. "Today, the coalition fights for everyone who has suffered from ISIL's inhumanity," Mr Obama said in a statement, adding that the group's "hateful ideology" would be banished to "the recesses of history".

Leaders around the world voiced outrage at the brutal killing. "It is incomprehensible how human beings are capable of such a cruel act," said German Chancellor Angela Merkel.

In the video, the burned man wore orange clothes similar to those worn by other foreign ISIS captives who have been killed since the US-led coalition started bombing the militants in July.

ISIS has previously released videos showing the beheadings of five US and British hostages and said that it killed two Japanese captives in the same way. It has meted out the same treatment to many more Arab prisoners, including Syrian government soldiers.

The militants have stepped up the gruesome killings while coming under increased military pressure from the air strikes and a ground campaign by Kurdish and Iraqi troops to reverse their territorial gains in Iraq and Syria.

ISIS emerged out of Al-Qaeda in Iraq. It expanded into Syria as the country was plunged into a civil war estimated to have killed 200,000 people since 2011.

The Syrian Observatory for Human Rights monitoring group said on Tuesday that 51 civilians, including children, had been killed by Syrian air force strikes inside the country within the past day.

The US-led coalition says it does not coordinate with the Syrian government of President Bashar al-Assad, described by Washington as part of the problem. It does work with the Iraqi government, which is also fighting ISIS.