The 26-year-old former US soldier was paraded at the end of an IS video released on Friday that showed the murder of British aid worker Alan Henning.
Hostages threatened at the end of four previous, near-identical IS beheading videos have subsequently been murdered.
Kassig's letter referred to his conversion to Islam during captivity, which his parents Ed and Paula Kassig said took place voluntarily at some point between October and December 2013 when he shared a cell with a devout Syrian Muslim.
Kassig also took the Muslim name Abdul-Rahman, and has been following the religion's practices, such as praying five times a day.
Also Read
"We see this as part (of) our son's long spiritual journey," his parents said in a statement released Saturday.
IS has justified killing Western hostages as retaliation for US-led air strikes on the group over swathes of territory it has seized in Iraq and Syria.
"We continue to pressure the government to stop its actions and continue to call on his captors to have mercy and release him," the Kassigs said in releasing portions of their son's June 2 letter.
"I am obviously pretty scared to die but the hardest part is not knowing, wondering, hoping and wondering if I should even hope at all. I am very sad all this has happened and for what all of you back home are going through," Kassig writes in the letter.
"If I do die, I figure that at least you and I can seek refuge and comfort in knowing that I went out as a result of trying to alleviate suffering and helping those in need."
His parents have said he had disappeared in Syria on October 1 last year.
"In terms of my faith, I pray every day and I am not angry about my situation in that sense. I am in a dogmatically complicated situation here, but I am at peace with my belief," Kassig wrote.
The letter ends with a simple: "I love you.