The family of murdered Isis hostage Kayla Mueller say they are “grateful” for the raid that killed Abu Bakr al-Baghdadi, the leader of the Islamic caliphate who repeatedly raped the Arizona native after her kidnapping in 2013.

The operation, which was named after Mueller, took place over the weekend, and was announced by Donald Trump on Sunday morning during a nationally broadcast statement.

Marsha Mueller, Kayla's mother, said that she learned about the death from that broadcast, and said the president’s words had moved her.

“We are deeply touched by what he said. We were grateful that they didn’t mess around and went right in,” Ms Mueller told CNN in a phone interview.

Kayla Mueller was imprisoned by Isis before being killed in a 2015 airs trike at the age of 26.

She had travelled to the Turkey/Syria border to work with the Danish Refugee Council and the humanitarian organisation Support to Life in 2012. She was then taken hostage by Isis in Aleppo in 2013, after visiting a Spanish Doctors Without Borders hospital.

The family was told four months after Kayla’s death that she was raped repeatedly by Baghdadi. Her body has yet to be found.

Carl Mueller, the father, told KPHO-TV that the news of the Isis leader's death left him in shock.

“It was a shock of course,” he said. “One minute you’re sitting here watching a movie, and the next minute you get the news the man that raped and possibly murdered your daughter has been killed.”

Ms Mueller told CNN that the news gives them hope that they will be able to finally get some answers about her daughter’s death, and to bring her home.

“Because of that one per cent possibility, how do you completely give up until you have her home?” she asked. “We want Kayla home, and I know that sounds like an impossible task, but after what we’ve been through, the things that pop up and happen I believe we might just find her.”

Mr Mueller added: “We feel this is the moment. He’s been killed, some of his lieutenants have been captured, and who else would know what happened to Kayla but these people close to him? Somebody, and it may be one of these people who were captured yesterday, knows what happened and know who killed her.”