Jordan executed by hanging on Wednesday a jailed Iraqi woman militant hours after Islamic State fighters released a video appearing to show a captured Jordanian pilot being burnt alive in a cage, a security source and state television said.

The militants had demanded the release of the woman, Sajida al-Rishawi, in exchange for a Japanese hostage who was later killed.

Responding to the killing of pilot Muath al-Kasaesbeh, 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.

Al-Rishawi 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.

Ziyad Karboli, an Iraqi al Qaeda operative, who was convicted in 2008 for killing a Jordanian, was also executed at dawn, said the security source, who declined to be identified.

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

But the kingdom had insisted that they would only release the woman, whose tribal Iraqi relatives were close aides of the slain Jordanian leader of al-Qaeda in Iraq Abu Musab al-Zarqawi whom Islamic State hold in high esteem as their mentor, as part of a deal to release the pilot.

Jordan said on Tuesday after it confirmed the death of the pilot that he had been killed a month earlier to counter domestic criticism that it could have done more to engage Islamic State in a deal that could have saved his life.

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

The fate of 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 they say was waged to serve the West's interests against Muslims.

Some also felt it could provoke a militant backlash.

Several politicians and lawmakers have called on the government to pull out of the coalition. The authorities said his death would not weaken resolve to fight militant Islamist groups.

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.

The Jordanian pilot is the first from the coalition known to have been captured by Islamic State. - Reuters