Kayla Mueller (Family photo)

The Islamic State claimed that a 26-year-old Arizona woman taken hostage by the group in Syria was killed Friday when a Jordanian fighter plane bombed a building where she was being held.

The claim could not be immediately verified, nor was it clear that Jordanian planes had bombed that location, described as being near Raqqa, the group’s de facto capital. The group released photos showing rubble of a building it claimed had been struck in airstrikes, but no images of the hostage, Kayla Mueller.

“The criminal Crusader coalition aircraft bombarded a site outside the city of ar-Raqqah today at noon while the people were performing the Friday prayer,” the Islamic State said in a statement, according to SITE Intelligence Group, which tracks online postings by Islamist militant groups. “The air assaults were continuous on the same location for more than an hour.”

The statement included Mueller’s phone numbers and other personal information.

Mueller would be the fourth American hostage to die since August while being held by the Islamic State. Her name had previously not been made public at the urging of her family and the FBI, which feared the disclosure could put her in greater danger.

Mueller had moved to an area along Turkey’s border with Syria in late 2012 and worked for a humanitarian organization, known as Support to Life, helping families fleeing the violence in Syria.

In August 2013, she was leaving a hospital run by Spanish Doctors Without Borders in the Syrian city of Aleppo when she was kidnapped. Mueller’s family later ­received proof-of-life evidence from her captors as well as an e-mail demanding a ransom of several million euros, according to individuals familiar with the case. The group threatened to kill her if the ransom was not paid by mid-August.

Speaking at an event in Washington, national security adviser Susan E. Rice said U.S. officials did not have any information to corroborate the claim that Mueller had been killed. Jordan’s military issued a brief statement confirming that its air force had carried out multiple strikes against the Islamic State on Friday but providing no other detail.

In an interview, a senior Jordanian official expressed skepticism about the Islamic State’s claim and said that the building pictured in the image distributed by the group was a “weapons warehouse.”

The official, Mohammad ­al-Momani, Jordan’s media affairs minister, did not indicate how he knew that or say whether the building had been targeted by the Jordanian military or other members of the U.S.-led coalition in Iraq and Syria.

Instead, Momani said that the latest Islamic State claim was “part of their media spinning/PR campaign, and it’s not the first time they do this.” The militants, he said, “are constantly trying to drive a wedge in the coalition [and] playing with public opinion. We need to be careful not to fall into this trap.”

He questioned how the Islamic State would have been able to identify any warplanes as Jordanian at such an altitude.

A U.S. intelligence official said authorities were mindful of the possibility that the Islamic State might claim that a hostage had been killed in an airstrike by the U.S.-led coalition. The official, speaking on the condition of anonymity because of the sensitivity of the matter, said there were no negotiations with the Islamic State.

Although Arab nations, including Jordan, have participated in what have been about 1,000 coalition airstrikes in Syria since September, the vast majority of them have been carried out by the United States.

Jordan vowed to step up its own airstrikes after the Islamic State released a video Tuesday depicting the burning death of a Jordanian fighter pilot, Lt. Muath al-Kaseasbeh, who had crashed in Syria. The United Arab Emirates, which suspended airstrikes after Kaseasbeh was shot down, is expected to resume them in the coming days, U.S. officials say.

None of the strikes announced by Central Command in recent days have indicated targets near Raqqa, a city in north-central Syria where the coalition has been reluctant to drop bombs because of the risk of civilian casualties.

A Central Command spokesman said in a statement that officials would be “unable to confirm details on any of today’s airstrikes” until Saturday.

Mueller was believed to have been held with other Islamic State hostages. Nicolas Henin, a French journalist who was freed in April, said in a message on Twitter on Friday that Mueller was “among the very last of my former cellmates still detained.”

“I was full of hope she could have a way out,” he said.

In early July, U.S. Special Operations forces launched a rescue attempt to save Western hostages thought to be held near Raqqa. The commandos, however, found no hostages at the site of the raid.

Based on evidence collected at the site, including strands of hair believed to be from Mueller, U.S. intelligence concluded that American captives had been there but had been moved a day to a week before the raid, according to a U.S. official familiar with the operation.

The Islamic State is believed to still be holding John Cantlie, a British journalist, and others. The group is known to have killed three Americans and two Britons.

Mueller’s parents issued a statement Friday evening expressing hope that she may still be alive and urging her captors to contact them privately.

“You told us that you treated Kayla as your guest, as your guest her safety and wellbeing remains your responsibility,” Carl and Marsha Mueller said in the statement.

The Obama administration, whose policy has been not to negotiate or agree to concessions with hostage-takers, is continuing an internal review, ordered by President Obama, of how the United States deals with hostage crises. Speaking at the Brookings Institution on Friday, Rice said that that refusal is not part of the review and will not be changed.

Instead, she said, officials are looking at “how we can support and be more responsible to the needs of the families” enduring a hostage taking and how “within the confines of the non-concessions policy, we might do better.”

Mueller, a native of Prescott, Ariz., had a desire to help the disadvantaged dating back to high school. She volunteered with the Save Darfur Coalition, writing letters and calling members of Congress, according to an article in the Daily Courier, the Prescott newspaper.

She told the newspaper in 2007, “I always feel that no matter how much I give I always get back more through these projects.”

Mueller graduated from Northern Arizona University in Flagstaff in 2009. After college, she traveled to India, working in an orphanage and teaching English to Tibetan refugees.

In 2011, she returned to Arizona, volunteering at a women’s shelter and working at an
HIV/AIDS clinic. Later that year, she flew to France to become an au pair, or domestic assistant, with the goal of learning French and then working in Africa. Instead, she decided she wanted to help families caught in the Syrian conflict and headed to Turkey.

In May 2013, she briefly returned to Arizona and appeared at an event at the Prescott ­Kiwanis ­Club, where she talked about her time helping Syrian children at refugee camps and her frustration with the situation in the war-torn country.

“When Syrians hear I’m an American, they ask, ‘Where is the world?’ All I can do is cry with them, because I don’t know,” she said.

William Booth in Amman, Jordan, and Carol Morello in Munich contributed to this report.