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The family of American hostage Kayla Mueller have confirmed she has been killed after they were reportedly sent a picture of her dead body by her ISIS captors.

The news of 26-year-old's death came four days bloody Islamic State militants said she had killed been by a coalition air strike near Raqqa, Syria.

According to report in the US the photograph showed the aid worker had died "recently" but the cause and exact nature of her death was unknown.

So far officials have yet to confirm the picture's authenticity.

(Image: REUTERS/Mueller Family/Handout via Reuters)

After being told of their loss her parents Carl and Marsha, and brother Eric, said they were "heartbroken" by the news.

"Kayla was a compassionate and devoted humanitarian. She dedicated the whole of her young life to helping those in need of freedom, justice, and peace," they said.

"We are heartbroken to share that we've received confirmation that Kayla Jean Mueller, has lost her life."

They then released a poignant hand-written note by Kayla which she penned during her 18-month captivity.

"I have been shown in darkness, light + have learned that even in prison, one can be free. I am grateful. I have come to see that there is good in every situation, sometimes we just have to look for it," it read.

After graduating from university in 2009, Kayla, who was kidnapped in Aleppo, Syria, in August 2013, travelled to northern India, Palestinian territories and Israel to assist humanitarian groups.

She then went to Syria to help people whose lives had been torn apart by war, concentrating on children.

"Syrians are dying by the thousands and they're fighting just to talk about the rights we have," Kayla, from Prescott, Arizona, said. For as long as I live, I will not let this suffering be normal."

Islamic State militants previously demanded a £4million ransom for her release but the US Government refused saying they do not negotiate or exchange prisoners with ISIS.

After the Mueller family made their statement President Barack Obama paid tribute to Kayla saying she "represents what is best about America".

"No matter how long it takes, the United States will find and bring to justice the terrorists who are responsible for Kayla's captivity and death," Mr Obama said.

"ISIS is a hateful and abhorrent terrorist group whose actions stand in stark contrast to the spirit of people like Kayla.

"On this day, we take comfort in the fact that the future belongs not to those who destroy, but rather to the irrepressible force of human goodness that Kayla Mueller shall forever represent."

Neither the White House nor Kayla's parents said how they received confirmation of the aid worker's death.