The Frasier star's younger sister Karen was abducted, raped, and murdered by serial killer Freddie Glenn in 1975, and he is currently serving a life term at the Buena Vista Correctional Facility in Colorado.
On Tuesday, Grammer testified at the parole hearing for Glenn via video conference, helping the board to decide whether the killer will remain behind bars for the crime he committed 39 years ago.
According to The Denver Post, Glenn appeared tearful at times while talking to Grammer, who accepted his apology, saying: "I want to believe you have actually changed your life. Things you say, I accept a lot of it.
"I accept that you live with remorse. But I live with tragedy every day."
The actor asked Glenn: "If someone did to your sister what you did to mine, what would you think should be done to him?"
The inmate replied: "I would be hurt, and I would be angry... I would like to think one day I would forgive."
Grammer responded: "You could not have come to a better person in the world than me to advocate for someone who has made some bad choices.
"I accept your apology. I forgive you. However, I cannot give your release my endorsement. To give that a blessing would be a betrayal of my sister's life."
The board has yet to make a decision on Glenn's parole.