The woman was identified as Kayla Jean Mueller, an American who went to Syria to do aid work, but there was no independent verification of the militants' claim. The statement appeared on a militant website commonly used by the group and was also distributed by Islamic State-affiliated Twitter users.
The 26-year-old Mueller, of Prescott, Arizona, is the only known remaining US hostage held by the Islamic State group.
A 2007 article about Mueller from the same newspaper said she was a student at Northern Arizona University and was active in the Save Darfur Coalition. A statement from the office of Sen. John McCain, R-Ariz, said Mueller graduated in 2009 and had worked to help people in need in India, Israel, the Palestinian territories and in Arizona.

On Sunday, Obama said the US was "deploying all the assets that we can" to find Mueller. If her death in yesterday's airstrike is confirmed, she would be the fourth American to die while being held by Islamic State militants. Three other Americans – journalists James Foley and Steven Sotloff, and aid worker Peter Kassig - were beheaded by the group.
Journalist Austin Tice, of Houston, Texas, disappeared in August 2012 while covering Syria's civil war. It's not clear what entity is holding him, but it is not believed to be the Islamic State group or the Syrian government, his family has said.
The announcement was the second time this week that extremists announced the death of a hostage. They released a video on Tuesday showing Jordanian air force Lt Muath al-Kaseasbeh, also 26, being burned to death in a cage in gruesome images that caused outrage in Jordan and the rest of the region.
Al-Kaseasbeh, whose F-16 came down in December while conducting airstrikes as part of a campaign against the militants by a US-led coalition, was believed to have been killed in early January.

Friday's statement said Mueller was killed in the militants' stronghold of Raqqa in northern Syria during Muslim prayers - which usually take place around midday – in airstrikes that targeted "the same location for more than an hour".
It published photos purportedly of the bombed site, showing a severely damaged three-story building, but offered no proof or images of Mueller.

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