U.S. intelligence officials are investigating a claim by ISIS that its sole known remaining American hostage, an aid worker held for nearly a year and a half, has been killed, and the terrorist group's claim that her death came in a Jordanian airstrike, sources told Fox News.

Kayla Mueller, 26, whose identity had previously not been revealed at the request of the U.S. government and her family as the Pentagon worked to secure her, is believed to be the last American hostage the terrorist army is holding, since the beheading of Peter Kassig, a 26-year-old American aid worker, killed in November. In its statement, ISIS also claimed Mueller was the only person killed in the airstrike, claiming none of its fighters injured or killed.

“We are obviously deeply concerned by these reports," said National Security Council spokeswoman Bernadette Meehan. "We have not at this time seen any evidence that corroborates ISIL’s claim.”

Late Friday night, the Mueller family released a statement saying "we are still hopeful that Kayla is alive." Addressing those who held Kayla, her family said,"We have sent you a private message and ask that you respond to us privately. We know that you have read our previous communications."

Images of children suffering in the early stages of Syria's ongoing civil war prompted Mueller, 26, to leave her home in Prescott, Ariz., in December, 2012,  to work with the Danish Refugee Council and the humanitarian organization Support to Life to help refugees. According to a family spokesperson, Kayla found the work heartbreaking but compelling.

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"For as long as I live, I will not let this suffering be normal, something we just accept," Mueller told her hometown newspaper, The Daily Courier, in a 2013 interview during a trip home to her family. "It's important to stop and realize what we have, why we have it and how privileged we are. And from that place, start caring and get a lot done."

She was captured on Aug. 4, 2013, in Aleppo, Syria, while leaving a Spanish hospital staffed by the international humanitarian group Doctors without Borders. 

"For as long as I live, I will not let this suffering be normal, something we just accept."

- Kayla Mueller, 2013 interview

Unlike other Islamic State captives killed by the group after their ransom demands were spurned, Mueller has not been featured on any hostage videos in which the terror army's prisoners, under obvious duress, denounce the West and plead for their lives. In some cases, intelligence officials have determined the hostages were killed long before the Islamic State militants claimed, raising the possibility that Mueller was already dead.

Just last Sunday, President Obama said the U.S. is doing everything it can to free Mueller.

"Obviously this is something that is heartbreaking for the family and we want to make sure we do anything we can to make sure that any American citizen is rescued from this situation," Obama told NBC in an interview that aired prior to the Super Bowl.

Jordan, which had previously taken part in U.S.-led airstrikes against Islamic State, stepped up its efforts on Wednesday, a day after the Islamic State released a horrifying video of a Jordanian air force pilot being burned to death in a cage. The Arab nation promptly hanged two terror suspects ISIS had sought to free and then, as King Abdullah II vowed to crush the terrorist army that has seized a bloody realm spanning parts of Syria and Iraq, mounted what it called devastating strikes against ISIS targets in Syria Wednesday, Thursday and Friday. It was in one of those strikes that Islamic State claims the woman was killed.

A Jordanian government spokesperson told Fox‎ News it is impossible to verify Mueller's death, but said officials are highly suspicious. The spokesman said he doesn't know what the hostage would have been doing in the location where the airstrike occurred.

Islamic State militants had demanded a $6 million ransom and the release of terrorist prisoners in exchange for Mueller. Among the prisoners Islamic State sought to trade for the woman was Aafia Siddiqui, a neuroscientist trained at MIT who was convicted of attempting to murder U.S. officials and planning to make dirty bombs for use in terror attacks in 2010.

According to Mueller's family, she graduated from Northern Arizona University in 2009, and planned to devote herself to humanitarian causes. From her college graduation through 2011, she lived and worked with humanitarian aid groups in northern India, Israel and Palestine. She returned home to Arizona in 2011, and worked for one year at an HIV/AIDS clinic while volunteering at a women’s shelter at night.

While her identity had not been reported in the media, friends, loved ones and officials in her home state have been comforting her family in recent months.

“While I have no new information today on Kayla’s current situation, I do know from speaking regularly with her family that she is extremely devoted to the people of Syria, and to doing all she can to alleviate the terrible suffering which has left more than 200,000 people dead and driven millions from homes into refugee status," said Den. John McCain, R-Ariz. "I also know that Kayla is extremely well-loved and dearly missed by her family and friends in Arizona."

If Mueller was indeed killed while held by ISIS, she would be the latest in a growing list of captives held until their deaths by the Islamist terror organization.

In August, an ISIS militant believed to be British and dubbed "Jihadi John" by the UK press, beheaded American freelance journalist James Foley in a video released online. That was followed by the similar, gruesome Sept. 2 murder of Steven Sotloff, another U.S. journalist who had written for Time magazine and other publications. Kassig was the last American known to have been killed by the barbaric group.

But Islamic State also beheaded two UK aid workers, David Haines, who was killed in September, and Alan Henning, who went to help refugees from Syria's bloody civil war, in October. Late last month, it released videos showing it had slaughtered two Japanese citizens, Haruna Yukawa, a self-employed security contractor, and Kenji Goto, a journalist.

Fox News' Shepard Smith, Martin Finn, Jennifer Griffin and Catherine Herridge contributed to this report.