Beirut,  Lebanon: Islamic State said on Friday that an American woman hostage it was holding in Syria was killed when Jordanian fighter jets bombed a building where she was being held, but Jordan expressed doubt about the Islamist militant group's account of her death.

In Washington, US officials said they could not confirm that the woman, 26-year-old humanitarian worker Kayla Mueller of Prescott, Arizona, had been killed.

Mueller was the last-known American hostage held by Islamic State, which controls wide areas of Syria and Iraq.

The group's latest claim, detailed by the SITE monitoring group, came just days after it released a video on Tuesday showing a captured Jordanian pilot, Mouath al-Kasaesbeh, being burned alive in a cage.

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Jordan's King Abdullah, who was in Washington discussing how to deal with Islamic State militants when the video was made public, vowed to avenge the pilot's death and ordered a stepped-up military role in the US-led coalition against the group. Jordan said it had carried out a second straight day of air strikes on Friday on Islamic State positions.

‘We are looking into it but our first reaction is that we think it is illogical and we are highly skeptical about it. ... It's part of their criminal propaganda,’ government spokesman Mohammad Momani said in response to Islamic State's account of what happened to Mueller.

Islamic State, in a message monitored by SITE, said Mueller died when the building in which she was being held outside Raqqa, a stronghold of the group, collapsed in a Jordanian air strike on Friday.

‘The air assaults were continuous on the same location for more than an hour," Islamic State said, according to SITE.

The group released photos of what it said were the building's wreckage but did not include photos of Mueller.

Reuters and other Western news organisations were aware Mueller was being held hostage but did not name her at the request of her family members, who believed the militants would harm her if her case received publicity.

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Mueller, a 2009 Northern Arizona University graduate, had a long record of volunteering abroad and was moved by the plight of civilians in Syria's civil war.

"For as long as I live, I will not let this suffering be normal - something we just accept," Mueller's local newspaper The Daily Courier quoted her in 2013 as saying.

Islamic State previously executed American journalists James Foley and Steven Sotloff and aid worker Peter Kassig, British aid workers David Haines and Alan Henning, Japanese journalist Kenji Goto and Goto's friend, Haruna Yukawa.

Among the hostages still thought to be held by the group is British photo journalist John Cantlie.