The parents of a US hostage who ISIL claimed had been killed in an airstrike said on Friday they were "hopeful" she was still alive and appealed to her captors to contact them.

The parents of a US hostage who ISIL claimed had been killed in an airstrike said on Friday they were "hopeful" she was still alive and appealed to her captors to contact them.

The militants said Kayla Jean Mueller had been buried under rubble after a raid by a Jordanian warplane in the Syrian city of Raqa, the extremists' self-proclaimed "capital."

But Washington said it had no proof to support the claim and refused to confirm her death as the parents of the 26-year-old aid worker from Arizona held out hope that she hadn't been killed.

"This news leaves us concerned, yet, we are still hopeful that Kayla is alive. We have sent you a private message and ask that you respond to us privately," Carl and Marsha Mueller said in a statement published on NBC News.  

They appealed for her safe return, and said they had previously been in touch with ISIL militants following her kidnapping in August 2013.

"You told us that you treated Kayla as your guest, as your guest her safety and wellbeing remains your responsibility," they said.

"Kayla's mother and I have been doing everything we can to get her released safely."

Meanwhile, Jordan -- still reeling from the brutal murder of one of its pilots by the Takfiri group -- also rejected the claim, calling it an "old and sick trick" to deter coalition strikes.

"The plane from the crusader coalition bombed a position outside the city of Raqa after Friday prayers," ISIL said in a statement posted on jihadist websites.

"No fighter was wounded but we can confirm that an American hostage was killed in the strikes."

The claim came as Amman said dozens of its jet fighters had struck ISIL, widening their campaign from Syria to include targets in neighboring Iraq.