Islamic State: Parents of Kayla Mueller 'hopeful she is alive'
The parents of a US hostage who Islamic State (IS) militants say was killed by a Jordanian air strike in Syria say they are "hopeful" she is still alive.
The parents of captured aid worker Kayla Jean Mueller urged IS to make contact with them, and to treat Ms Mueller as a "guest".
White House officials say they have seen no proof she was killed.
IS released images of a ruined building where it says she died, but no images of the aid worker herself.
It said that Jordanian jets had bombed the building on the outskirts of their Syrian stronghold, Raqqa.
Jordan, which carried out air strikes on IS targets in Syria on Thursday, dismissed the reports as propaganda.
Mentioning previous communications with IS in their statement, Ms Mueller's parents said they had decided to break their public silence at news of reports of their daughter's death.
"This news leaves us concerned, yet, we are still hopeful that Kayla is alive," they said.
"We have sent you a private message and ask that you respond to us privately. You told us that you treated Kayla as your guest, as your guest her safety and wellbeing remains your responsibility."
A graduate of Northern Arizona University, Ms Mueller, 26, first came to the Turkish and Syrian border in 2012 to work with refugees.
She was abducted while working in Aleppo, Syria, the following year.
If her death is confirmed, she would be the fourth American to die while being held by IS. Journalists James Foley and Steven Sotloff, and aid worker Peter Kassig were beheaded by the group.
A spokeswoman for US President Barack Obama's National Security Council said the US was "deeply concerned" by the reports of her death but added that officials had seen no evidence to confirm the IS report.
Analysis: Aleem Maqbool, BBC News, Washington
There are many who have raised doubts about Islamic State's claim that Kayla Mueller was killed in a coalition strike in Raqqa - in an attack in which none of its own fighters died, it says.
Jordan has increased its participation in the bombing of the militant stronghold since one of its pilots was shown being burned to death by IS militants, and officials in Jordan insist they will keep up the pressure. Saying a Western hostage has been killed by Jordan is being seen by some as an attempt to take the wind out of the sails of this renewed Jordanian resolve to fight the militants.
Claiming the coalition killed Ms Mueller could also provide a convenient solution to Islamic State's problem of what to do with a female hostage, one they might not want to be shown killing in the same barbaric way as they have others.
Unfortunately, the doubts about the veracity of the Islamic State claim will provide little comfort to Kayla Mueller's family and friends.
A Jordanian government official dismissed reports that the country's air force had killed Ms Mueller as "criminal propaganda", adding: "We think it's illogical and we are highly sceptical about it."
Thursday's strikes were carried out in response to the killing of a Jordanian fighter pilot by IS militants.
A video of Moaz al-Kasasbeh being burned alive in a cage had been posted online by IS. He was captured by militants in December after his F-16 fighter jet crashed in Syria.
Thousands rallied in Jordan's capital, Amman, on Friday morning in support of their government's military response.
Among those marching was Jordan's Queen Rania, who told the BBC the country was "united in our horror".