The family of slain aid worker and ISIS prisoner Kayla Mueller on Sunday praised President Trump and the commandos who pulled off the daring raid that killed ISIS leader Abu Bakr al-Baghdadi -- but also delivered a stinging rebuke regarding President Obama's handling of Mueller's capture.

Mueller, 26, was a humanitarian worker from Prescott, Ariz., who was captured while leaving a hospital in Aleppo, Syria, during that nation's bloody civil war in 2013. She is believed to have been tortured and raped by al-Baghdadi himself until her death 18 months later.

The mission that killed al-Baghdadi in his Idlib hideout this weekend was named after Mueller, National Security Adviser Robert O'Brien said Sunday morning on "Meet The Press."

“One of the things that Gen. [Mark] Milley, the chairman of the Joint Chiefs of Staff, did was named the operation that took down al-Baghdadi after Kayla Mueller, after what she had suffered,” O'Brien said. "And that was something that people should know. But justice was brought to those Americans who were so brutally killed, as were others, as the president pointed out."

Marsha Mueller, the woman's mother, praised President Trump and the Special Operations commandos who raided the compound and told the Arizona Republic that she believes if “Obama had been as decisive as Trump” her daughter may still be alive.

Kayla Mueller's parents said on Sunday that they hope the ISIS leader's death will reveal more answers about what happened to their daughter. Even though they confirmed her death through pictures sent by militants, their daughter's body was never recovered.

"She was held in many prisons," Carl Mueller, her father, told the Republic on Sunday. "She was held in solitary confinement. She was tortured. She was intimidated. She was ultimately raped by al-Baghdadi himself.”

"She was held in solitary confinement. She was tortured. She was intimidated. She was ultimately raped by al-Baghdadi himself." — Carl Mueller, Kayla's father

The Obama administration was criticized over a reported 2015 rescue mission that targeted four prisoners held at a makeshift ISIS prison.

By the time U.S. commandos stormed the compound, the hostages were already gone. Some relatives and people who worked on the raid blamed the White House for not acting swiftly enough on giving the mission a green light.

Specific intelligence had emerged in late May providing officials with the hostages' likely location -- including a building, sources told Fox News at the time. The intelligence was described as being '"strong," "specific" and "perishable," but the White House did not sign off on the rescue mission until much later, and it ultimately was launched July 4.

TRUMP KEPT RAID SECRET FROM PELOSI

President Obama said in a later interview that it was inaccurate to say the U.S. didn’t do everything it could to rescue the hostages. Susan Rice, his former national security adviser, said the approval process for the 2015 raid could not have been faster.

Trump, in the meantime, described the weekend raid in northwest Syria and said military helicopters flew over a territory now controlled by Russian and Syrian forces before it landed at the compound.

Trump described al-Baghdadi as dying "in a vicious and violent way, as a coward, running and crying.”

“He died like a dog, he died like a coward,” Trump said in a speech to the nation Sunday morning.

Trump said al-Baghdadi died after he detonated a suicide vest, killing himself. Trump said three children who were with al-Baghdadi were also killed in the blast. Eleven other young children were taken out of the location uninjured, Trump said.

“Our reach is very long,” Trump said. He pointed to the recent death of Hamza bin Laden, son of al-Qaeda leader Usama bin Laden. “These savage monsters will not escape their fate, and they will not escape the final judgment of God.”

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Trump said “Al-Baghdadi and the losers who work for him” had “no idea what they were getting into."

Carl Mueller, who was a supporter of Trump's 2016, told the Republic that the president knew his daughter's story.

"I don’t think anything would have stopped him from getting this guy," he said.

Fox News' Catherine Herridge and Ronn Blitzer and the Associated Press contributed to this report.