The Islamic State group has been blamed for the deaths of American hostages including journalist James Foley.
The vice president said the Obama administration "hesitated" to approve a raid to rescue American Kayla Mueller in Syria, allowing her ISIS captors to move her to a new location.
After news of ISIS leader Abu Bakr al-Baghdadi's death, Marsha Mueller on Sunday praised Trump for bringing justice for her daughter.
Mueller, a former humanitarian aid worker from Prescott, Arizona, was kidnapped by ISIS in August 2013 after she travelled from Turkey to Aleppo.
Nisreen Assad Ibrahim Bahar told the FBI that ISIS leader Abu Bakr al-Baghdadi "owned" Mueller during her captivity.
Umm Sayyaf was interrogated by U.S. for months, providing vital intelligence to Washington on the terror group.
A photograph provided to her family should mean her body was buried.
Mueller spent over a year in captivity, captured in Aleppo, Syria, in 2013.
"This news leaves us concerned, yet, we are still hopeful that Kayla is alive," they said in the message.