Kayla Mueller, a 26-year-old American woman held by fighters from the Islamic State in Iraq and the Levant (ISIL), has been confirmed dead, her parents and the Obama administration said Tuesday.

ISIL had said last Friday that she was killed in a Jordanian airstrike. However, the Pentagon said Tuesday that Mueller died at the hands of ISIL.

Navy Rear Adm. John Kirby was asked Tuesday if there was any doubt who killed the aid worker. He replied: "No doubt. ISIL."

Kirby said U.S. officials still don't know how Mueller died. But he added that officials are certain it was not in one of the airstrikes Jordan launched in retaliation for killing one of its pilots.

The White House said Mueller's family received a private message from her captors over the weekend. The information in the message was authenticated by the U.S. intelligence community.

"We are heartbroken to share that we've received confirmation that Kayla Jean Mueller has lost her life," her parents, Carl and Marsha Mueller, said in a statement. "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."

President Barack Obama said that Mueller, who has worked with Syrian refugees, "epitomized all that is good in our world."

"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," the president said.

Mueller was the only known remaining U.S. hostage held by ISIL. She was taken into captivity in August 2013 while leaving a hospital in Syria just days before her 25th birthday.

"The suffering of the Syrian refugees drew Kayla to the Turkish/Syrian border in December 2012 to work with Support to Life, the Danish Refugee Council and other humanitarian organizations to assist families who had been forced to flee their homes," her family said in a statement Tuesday.

"Kayla found this work heartbreaking but compelling; she was extremely devoted to the people of Syria."

Mueller's humanitarian work began long before Syria, her family said in a statement released to media. After her graduation from Northern Arizona University in 2009, Mueller worked with humanitarian aid groups in northern India, Israel and Palestine, the statement said. In 2011, she returned to Arizona to work for one year at an HIV/AIDS clinic while volunteering with a women's shelter at night, her family said.

In the fall of 2010, Mueller worked in Palestine with the International Solidarity Movement (ISM), a nonviolent activist group that uses direct action to oppose the Israeli occupation, the group said in a statement released Monday. Mueller demonstrated with Palestinians peacefully resisting confiscation and demolition of their homes and lands, the ISM statement said.

"I could tell a few stories about sleeping in front of half demolished buildings waiting for the one night when the bulldozers come to finish them off ... I could tell a few stories about walking children home from school because settlers next door are keen to throw stones, threaten and curse them," Mueller wrote in online posts while working in Palestine.

Al Jazeera and wire services