Islamic State militants released a video on Tuesday appearing to show a captured Jordanian pilot being burnt alive in a cage, a killing that shocked the world and prompted Jordan to promise an "earth-shaking" 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.

A Jordanian official said 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.

The Islamic State militant group said on Friday that an American female hostage it was holding in Syria had been killed when Jordanian fighter jets hit a building where she was being held, the SITE monitoring group said.

In Washington, U.S. officials said they could not confirm that the woman, who has been identified as Kayla Mueller, had been killed.

State Department spokeswoman Marie Harf told reporters during a briefing in Washington that "I cannot confirm those reports in any way."

"We have said that there are a number of Americans being held overseas, including still by the Islamic State. I'm not going to get into further details than that, Harf added.

"We are obviously deeply concerned by these reports. We have not at this time seen any evidence that corroborates ISILs claim," Bernadette Meehan, spokeswoman for the White House National Security Council, said in a statement, using an acronym for the group.

Jordan's air force chief said on Sunday his country's jet fighters had conducted 56 bombing raids in three days against Islamic State militants in northeast Syria, targeting key bases and arms depots.

"We achieved what we aimed for. We destroyed logistics centers, arms depots and targeted hideouts of their fighters," General Mansour al-Jbour, head of the Jordanian airforce, told a news conference.

The raids had "degraded" nearly 20 percent of the militants' capabilities, he said.

At least 7,000 militants had been killed in the last few weeks of coalition bombing, he said.

No new strikes were announced for Sunday.

President Barack Obama and the family of U.S. aid worker Kayla Mueller confirmed on Tuesday that the last-known American hostage held by Islamic State militants had died, with Obama promising to "find and bring to justice the terrorists who are responsible."

U.S. officials said the family received an email and photograph over the weekend from her captors that confirmed her death but said the circumstances in which she died remained unclear.

Mueller, 26, was captured in August 2013 while leaving a hospital in the northern Syrian city of Aleppo. She previously had been working in Turkey providing humanitarian assistance to refugees from Syria's bloody civil war.

Two men have been charged in Australia after police thwarted an imminent terror attack, seizing an Islamic State flag, a machete and an Arabic-language video detailing the alleged plot during a raid in Sydney.
New South Wales Deputy Police Commissioner Catherine Burn said the planned attack was consistent with the messaging coming out of IS, while New South Wales state Premier Mike Baird described it as beyond disturbing.
Asked whether the plot involved a beheading, Burn said police were as yet unsure, but that it had been due to happen Tuesday in Sydney, and would likely have involved a knife.
The men, Omar Al-Kutobi, 24, and Mohammad Kiad, 25, were arrested in a raid on a property in the citys western suburbs by the Joint Counter Terrorism Taskforce on Tuesday after a tip-off, and charged with making preparations for a terrorist act.
Reportedly devout Muslims, they were refused bail with the case adjourned until Thursday due to security issues.
A number of items were located including a machete, a hunting knife, a home-made flag representing the proscribed terrorist organisation IS, and also a video which depicted a man talking about carrying out an attack, Burn said.
We will allege that both of these men were preparing to do this act yesterday. We built up information, we received further information which indicated an attack was imminent. And we acted.
Attorney-General George Brandis told parliament the video allegedly showed one suspect kneeling in front of an ISIL flag, with the knife and machete, making a politically motivated statement, threatening to undertake violent acts with those weapons.
ISIL is another name for the Islamic State group.
Prime Minister Tony Abbott said the video was in Arabic and that regrettably there are people out there, some living in our midsts, who would do us harm.
But he added that the government was maintaining a ceaseless vigilance against such people.
Baird said a potentially catastrophic incident had been avoided.
It was beyond disturbing, what was planned, he told reporters. Certainly, something catastrophic was avoided yesterday and for that we should be very thankful.
Australia in September raised its terror threat level and carried out extensive raids in Sydney and Brisbane to disrupt an alleged plot by IS supporters to abduct and randomly behead a member of the public.

Islamic State said on Thursday it was holding an Israeli Arab who had posed as a foreign fighter in order to spy for Mossad, an account denied by Israel and by the man's family, who said he had been kidnapped.

In an interview published by Islamic State's online English-language magazine Dabiq, Muhammad Musallam, 19, said he had joined the insurgent group in Syria so as to report to the Israelis on its weapons caches, bases and Palestinian recruits.

After his conduct aroused the suspicion of Islamic State commanders, Musallam was quoted as saying, he broke cover by phoning his father in East Jerusalem, leading to his capture.

"I say to all those who want to spy on the Islamic State, don't think that you're so smart and that you can deceive the Islamic State. You won't succeed at all," he said, according to Dabiq.

"Stay away from this path. Stay away from helping the Jews and the murtaddin (apostates). Follow the right path."