The parents of an American aid worker held hostage by the Islamic State terror group reportedly did not want the U.S. to launch a mission to rescue her, but rather have her release negotiated.

Foreign Policy reported that as a result of the request, military plans to locate 26-year-old Kayla Mueller were shot down before President Obama had a chance to decide on a possible strategy to locate her.

The parents of Mueller reportedly told U.S. officials that such an operation would be "too risky."

ISIS said Friday that Mueller, of Prescott, Arizona, died in a Jordanian airstrike, but the government of Jordan dismissed the statement as “criminal propaganda” and the U.S. said it had not received any evidence to corroborate the report.

If the death 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.

The parents of Mueller released a statement late Friday addressing the terrorist group’s claim of their daughter’s death. They said the alleged death of their daughter concerned them, but they were still hopeful she was alive.

"You told us that you treated Kayla as your guest, as your guest her safety and well-being remains your responsibility," the statement from Mueller's parents says.

Mueller is an aid worker who has previously volunteered with aid groups in India, Israel and the Palestinian territories. Her identity had not been disclosed until now out of fears for her safety. Her family said she was taken hostage by the Islamic State group on Aug. 4, 2013, while leaving a hospital in Syria.

"The common thread of Kayla's life has been her quiet leadership and strong desire to serve others," Mueller's family said in the short statement released Friday.

Jordan has been launching airstrikes against the extremist group in response to a video released this week that shows captive Jordanian pilot Lt. Muath al-Kaseasbeh being burned to death in a cage.

Al-Kaseasbeh, whose F-16 came down in December while conducting airstrikes as part of a campaign against the militants by a U.S.-led coalition, was believed to have been killed in early January.

Friday's statement from the group 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.

The statement said no Islamic State militants were killed in the airstrikes, raising further questions about the veracity of the claim.

Jordanian government spokesman Mohammed al-Momani said it was investigating.

"But as a first reaction, we think it's illogical and we are highly skeptical about it. How could they identify a Jordanian warplane ... in the sky? What was the American lady doing in a weapons warehouse?" al-Momani said.

"It's part of their criminal propaganda. They have lied that our pilot is alive and tried to negotiate, claiming he is alive while they had killed him weeks before," he added.

American officials said they also were looking into the report.

“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."

The Associated Press contributed to this report

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