The parents of an American humanitarian worker held hostage by the Islamic State of Iraq and the Levant (ISIL) have reached out to the group after it claimed their daughter was killed in an air strike.

In a statement posted on sympathetic websites on Friday, ISIL said 26-year-old Kayla Mueller was buried beneath rubble after an air raid by a Jordanian fighter jet in Raqqa, in northern Syria.

In response, parents Carl and Marsha Mueller issued a statement through a family representative asking ISIL to contact the family privately, the Reuters news agency reported on Saturday.

"You told us that you treated Kayla as your guest, as your guest her safety and well-being remains your responsibility," they said in a message directed to "those in positions of responsibility for holding Kayla".

Rallies show support for Jordan air strikes against ISIL [Al Jazeera]

The Mueller's statement also said that they are hopeful that their daughter is still alive.

Mueller was taken captive in August 2013 in the Syrian city of Aleppo, after leaving a Medecins Sans Frontieres (Doctors Without Borders) hospital.

MSF said she had been visiting the facility with a friend contracted to do some repairs, and was detained as she headed to the bus station in Aleppo, from which she was meant to depart for Turkey.

No proof

The US said on Friday that it had not yet seen any proof to confirm ISIL's claim that Mueller had been killed.

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

Activists who monitor the Syrian conflict from inside the country said coalition planes hit several targets on the edges and outskirts of Raqqa in quick succession on Friday.

A Raqqa-based collective of anti-ISIL activists known as "Raqqa is Being Slaughtered Silently" said the jets targeted multiple ISIL positions and headquarters in the western and eastern countryside of Raqqa, sending up columns of smoke. Explosions could be heard in the city.

The collective said there were no recorded civilian casualties, and did not mention any ISIL casualties.

Air campaign widened

The claim about Mueller's death came on Friday as Jordan said it had widened its air campaign from Syria to include targets in neighbouring Iraq.

Jordan's Foreign Minister Nasser Judeh denounced ISIL's claim on Twitter as "an old and sick trick used by terrorists and despots for decades: claiming that hostages human shields held captive are killed by air raids".

ISIL has murdered both locals and foreigners, including two US journalists, an American aid worker, two British aid workers, two Japanese hostages and a Jordanian pilot.

Jordan promised a harsh response after ISIL released a video this week showing the burning alive of Moaz al-Kassasbeh, the Jordanian air force pilot.

Kassasbeh, whose F-16 jet came down in December while conducting air strikes, was believed to have been killed in early January.

Highly devoted

Mueller's parents, who live in Prescott, Arizona, said their daughter has devoted her career "to helping those in need in countries around the world" since graduating from Northern Arizona University in 2009.

She lived and worked with humanitarian aid groups in northern India, Israel and the Palestinian territories, before returning home to Arizona in 2011 and working at an HIV/AIDS clinic and a women's shelter.

The suffering of Syrian refugees prompted Mueller to head to the Turkey-Syria border in December 2012 to work with the Danish Refugee Council and the humanitarian group Support to Life, the family statement said.

When asked what drove her, Mueller once said: "I find God in the suffering eyes reflected in mine, if this is how you are revealed to me, this is how I will forever seek you."

Source: Agencies