PRESCOTT, Arizona — The parents of a 26-year-old woman who Islamic State extremists say has been killed in an airstrike in northern Syria have said in a statement addressed to group leaders that the claim of their daughter’s death concerned them but they were still hopeful she was alive.

The Islamic State group said on Friday that Kayla Jean 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 seen any evidence to corroborate the report.

Mueller is the only known remaining U.S. hostage held by the Islamic State group.

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.

“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.