The act of grace and forgiveness comes on the second anniversary of their daughter’s death in ISIS captivity.
But making peace with Doctors Without Borders was hard to swallow, her parents, Marsha and Carl, of Prescott, Arizona, told ABC News.
"It is difficult, but ultimately this endowment is going to do what Kayla wanted done," her father said.
Marsha Mueller said she and her husband Carl made their decision after praying for Kayla Mueller to send a signal and looking at a Doctors Without Borders map that their daughter had displayed in college.
"I kept asking Kayla, we have this money, there is so much need in the world and we want to give it to someone, so who has the greatest reach around the world?" her mother said. "Doctors Without Borders is a great organization, I have a lot of respect for them and I knew of her respect for them."
Marsha and Carl Mueller said officials with Doctors Without Borders refused to speak with them for almost a year as they struggled to learn who held Kayla captive . The parents said that the officials later withheld for weeks critical information provided by freed hostages from the aid group -- information that directly concerned their daughter and they say was needed in order to begin negotiations for her release.
In a phone conversation recorded by the Muellers 10 months after their daughter's kidnapping and provided to ABC News, they asked the group if it would help negotiate for their daughter after Doctors Without Borders had ransomed out its own staff held by ISIS.
"No," the senior official replied. "So, the crisis management team that we have installed for our five people and that managed the case for our people will be closed down in the next week. Yeah? ... Because our case is closed."
"They're a fabulous organization, and they do wonderful work," Carl Mueller told ABC News' "20/20" in the interview broadcast last August, "but somewhere in a boardroom, they decided to leave our daughter there to be tortured and raped and ultimately murdered."
Their donation announced today will act as seed money for a new endowment there to further Kayla Meuller's desire to help mothers and children harmed by war, famine and disaster in 70 countries.
"This wouldn't have happened if Doctors Without Borders hadn't come to their house and sat with their anger. They felt the full force of it," recalled the Muellers' friend and most important adviser, Rev. Kathleen Day of Northern Arizona University's campus ministry, who also was close to their daughter when she attended college there.
One of Doctors Without Borders' senior officials who went to Prescott and experienced the brunt of their pain and anguish was Jason Cone, who leads the organization's U.S. chapter.
“The Mueller family’s decision to establish an endowment with MSF in memory of their daughter is an act of great and humbling generosity," said Cone, executive director of Doctors Without Borders' New York office.
In a statement to ABC News, Cone said “MSF expresses its deepest sympathies to Kayla’s family and friends. We mourn her passing and we are honored to help keep her memory alive.”
The new endowment, “Kayla’s Hands – the Kayla Mueller Memorial Endowment Fund,” will be administered by the aid group's New York office and will support their global medical and humanitarian aid programs, Cone said.
The Muellers tell ABC News that donations poured in following an ABC News "20/20" documentary, "The Girl Left Behind" last August, in which the Muellers shared their frustrations over U.S. government efforts to block them from paying ISIS a ransom for their daughter.
Nearly half of the money to be donated today came from viewers of the program, the parents said.
The parents also that President Obama had failed to deliver a personal contribution he had promised to the foundation for 18 months.
Obama sent the family an apologetic letter and a personal check after the ABC broadcast, joining hundreds of viewers who sent contributions, such as a class full of underprivileged school kids in Utah who taped dollar bills to letters of support they wrote.
The long, terrible ordeal endured by the Prescott, Arizona couple -- an auto body shop owner and a former nurse -- began Aug. 4, 2013 with 24-year old Kayla Mueller's abduction in war-torn Aleppo, Syria.
It eventually led to an intense negotiation with the infamous terror group , which saw the hostage's mother and father trading emails with militants from a laptop on their kitchen counter, with the FBI's assistance.
Cone, the group's U.S. director, was not directly involved in the decisions that affected Kayla Mueller at the time . B ut in August he defended the aid group's actions, insisting they had to negotiate for their staffers' freedom with ISIS and couldn't do the same for someone who did not work for them.
"I don't think there was a moral responsibility," Cone said in an interview with ABC News last August. "We can't be in the position of negotiating for people who don't work for us."
Cone said Mueller had not been asked by the group to come to Syria and would have not have permitted her to travel there if it had been asked because of her American citizenship.
Today, Cone made a point of praising the woman her fellow hostages described as selfless and who often put their wellbeing before her own.
“Based on what I have learned about Kayla from her family and her writings, she was incredibly compassionate, devoted, and connected to neglected people. Kayla’s legacy will live on every day, in part through the formation of this endowment and the support it will provide to MSF’s medical work throughout the world," Cone said.
The aid group also ran into trouble with two of its former staff who were held in an abandoned oil refinery south of Raqqa, Syria, with Kayla. Two abducted women, Frida Saide and Patricia Chavez, said that they had not been told by a Doctors Without Borders' security expert that there had been kidnappings of their staff in Syria several months before they entered the lawless country to do aid work. They were shocked to learn about it when Kayla Mueller shared a cell with them in early 2014.
Doctors Without Borders in a statement last August offered conflicting reasons why the women weren't informed of Kayla's kidnapping before they faced a similar risk. One explanation offered was that they weren't near Aleppo -- which the former staffers immediately disputed, saying they traveled trough the city when they entered Syria from Turkey.
Kayla Mueller's family said that the aid group refused to speak with them for 10 months, and when they did finally speak, the family said that they learned that Doctors Without Border had been withholding for seven weeks a letter and an email address for ISIS militants intended to begin negotiations.
That letter and contact information had been smuggled out by Chavez and Saide. Doctors Without Borders claimed last year that the two women had been instructed by Kayla Mueller to not hand over the letter and email address while two male Doctors Without Borders staff remained captive.
Saide told ABC News last year that the statement by her former employer was "not true." Chavez agreed, saying, "There was no discussion where Kayla asked us not to pass it on."
Given all of this, Saide today said it was both surprising and unexpected when the Muellers recently shared with her their plans to donate most of the money they have collected for the Kayla's Hands Foundation to the organization they felt had failed their daughter.
"It was not something that I could immediately get my head around," Saide told ABC News today. "But they are Kayla's parents, and just as Kayla did, they impress me with their kindness and generosity. I admire them so much and am full of respect for their decision."
Faith is strong with the Mueller family, the parents say. Other hostages said that they once witnessed Kayla Mueller correcting ISIS executioner "Jihadi John," when he told other hostages she had converted from Christianity to Islam.
With the family's faith comes forgiveness for Doctors Without Borders and its past decisions regarding Kayla, her parents say.
"I've forgiven them. I'll never forget," Marsha said.
"It was never our intention to harm Doctors Without Borders but only to hold them accountable," Carl explained. "They've stepped up to the plate. Hopefully this gesture will make changes and the next person in this situation will come home."