Middle East
6 February 2015
Last updated at 18:45 ET
No proof has been offered other than a photo of a ruined building.
Jordan, which carried out air strikes on IS targets in Syria on Thursday, dismissed the report as propaganda.
A graduate of Northern Arizona University, Ms Mueller, 26, first came to the Turkish/Syrian border in 2012 to work with refugees.
She was abducted while working in Aleppo, Syria the following year.
According to IS, she was killed in the building where she was being held. It did not provide images of a body.
If her death is confirmed, she would be the fourth American to die while being held by IS. Journalists James Foley and Steven Sotloff, and aid worker Peter Kassig, were beheaded by the group.
A spokeswoman for US President Barack Obama's National Security Council said the US was "deeply concerned" by the reports but added that officials had seen no evidence to corroborate the IS report.
Analysis: Aleem Maqbool, BBC News, Washington
There are many who have raised doubts about Islamic State's
claim that Kayla Mueller was killed in a coalition strike in Raqqa - in
an attack in which none of its own fighters died, it says.
Jordan has increased its participation in the bombing of the militant stronghold since one of its pilots was shown being burned to death by IS militants, and officials in Jordan insist they will keep up the pressure. Saying a Western hostage has been killed by Jordan is being seen by some as an attempt to take the wind out of the sails of this renewed Jordanian resolve to fight the militants.
Claiming the coalition killed Ms Mueller could also provide a convenient solution to Islamic State's problem of what to do with a female hostage, one they might not want to be shown killing in the same barbaric way as they have others.
Unfortunately the doubts about the veracity of the Islamic State claim will provide little comfort to Kayla Mueller's family and friends.
Profile: 'Dedicated' aid worker
Islamic State's asymmetry of fear
'Criminal propaganda'
A Jordanian government official dismissed reports that the
country's air force had killed Ms Mueller as "criminal propaganda",
adding: "We think it's illogical and we are highly sceptical about it."
Raqqa was among areas targeted by Jordanian air strikes on Thursday.
The strikes were carried out in response to the killing of a Jordanian fighter pilot by IS militants.
A video of Moaz al-Kasasbeh being burned alive in a cage had been posted online by IS.
He was captured by militants in December after his F-16 fighter jet crashed in Syria. The video is believed to have been filmed on 3 January.
Thousands rallied in Jordan's capital, Amman, on Friday morning in support of their government's military response.
Among those marching was Jordan's first lady, Queen Rania, who told the BBC the country was "united in our horror".
Thousands rally in Jordan
by Nasra Ismail, Melissa Gruz, and Biodun Iginla, BBC News
Jon Sopel in Washington: "It may be that this is more propaganda than fact"
White
House officials say they have not seen any evidence to confirm reports
by the Islamic State (IS) militant group that an air strike killed a US
hostage.
The group says a female hostage, Kayla Jean Mueller, was
killed when Jordanian jets bombed a house on the outskirts of their
Syrian stronghold, Raqqa.No proof has been offered other than a photo of a ruined building.
Jordan, which carried out air strikes on IS targets in Syria on Thursday, dismissed the report as propaganda.
A graduate of Northern Arizona University, Ms Mueller, 26, first came to the Turkish/Syrian border in 2012 to work with refugees.
She was abducted while working in Aleppo, Syria the following year.
According to IS, she was killed in the building where she was being held. It did not provide images of a body.
If her death is confirmed, she would be the fourth American to die while being held by IS. Journalists James Foley and Steven Sotloff, and aid worker Peter Kassig, were beheaded by the group.
A spokeswoman for US President Barack Obama's National Security Council said the US was "deeply concerned" by the reports but added that officials had seen no evidence to corroborate the IS report.
Jordan has increased its participation in the bombing of the militant stronghold since one of its pilots was shown being burned to death by IS militants, and officials in Jordan insist they will keep up the pressure. Saying a Western hostage has been killed by Jordan is being seen by some as an attempt to take the wind out of the sails of this renewed Jordanian resolve to fight the militants.
Claiming the coalition killed Ms Mueller could also provide a convenient solution to Islamic State's problem of what to do with a female hostage, one they might not want to be shown killing in the same barbaric way as they have others.
Unfortunately the doubts about the veracity of the Islamic State claim will provide little comfort to Kayla Mueller's family and friends.
Profile: 'Dedicated' aid worker
Islamic State's asymmetry of fear
Raqqa was among areas targeted by Jordanian air strikes on Thursday.
The strikes were carried out in response to the killing of a Jordanian fighter pilot by IS militants.
A video of Moaz al-Kasasbeh being burned alive in a cage had been posted online by IS.
He was captured by militants in December after his F-16 fighter jet crashed in Syria. The video is believed to have been filmed on 3 January.
Queen Rania of Jordan: "We cannot win this war alone, but it is absolutely our war"
Among those marching was Jordan's first lady, Queen Rania, who told the BBC the country was "united in our horror".
Thousands rally in Jordan
Islamic State
Features and Analysis
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The murder of Jordanian pilot Moaz al-Kasasbeh is part of Islamic State's strategy to terrify opponents by releasing sadistic videos, argues Shiraz Maher.
Asymmetry of fear
-
Kobane unbeaten
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What is IS?
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Key countries
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Why is IS so violent?
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Can IS be defeated?
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Rare visit reveals 'brutal' IS
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Sex-slavery trauma
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How extremist groups raise money
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Mosul diaries: Poisoned by water
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Yazidis' tales of survival
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What the Kassig video tells us
From other news sites
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CBC Jordan airstrike kills U.S. hostage, ISIS claims read comments 28 mins ago
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Japan Today IS claims Jordan airstrike kills female U.S. hostage 1 hr ago
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Miami Herald Islamic State says airstrike killed US hostage, US skeptical 2 hrs ago
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Reuters UK Islamic State says U.S. hostage killed in air strike in Syria 3 hrs ago
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Huffington Post UK Islamic State Claims American Aid Worker Kayla Mueller Was Killed By Jordanian Airstrike On Raqqa 6 hrs ago
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