A distraught Harrison appeared on a video link from the Hamilton County Jail during Thursday's appearance on a murder charge in Hamilton Superior Court.
When Magistrate David Najjar read him his rights, Harrison said, "What about a right to a rope?"
"I killed my poor little baby. Please kill me," Harrison begged.
Najjar entered a not guilty plea on Harrison's behalf and appointed him an attorney. He also ordered Harrison held without bond in the jail pending a March 12 trial date.
Hamilton County Prosecutor Lee Buckingham said he will consider seeking life without parole for Harrison.
Noblesville Police Detective Michael Sadler said in a probable cause affidavit that officers found the toddler with two knife-stab wounds to his chest and one stab wound from a nail puller in the forehead. Medics pronounced the boy dead Wednesday afternoon at the family's apartment about 15 miles north of Indianapolis.
The boy's grandmother, Pamela Harrison, told officers that "Micah stated that someone or something was trying to kill him" and that he hit a closet with a hammer, which she took from him, telling the man no one was there.
After she hid the hammer in a bedroom, she saw her son "moving quickly from the kitchen to the other bedroom where she knew Michael was playing." She found her son atop the boy, who was lying on the floor, and watched him stab Michael with the knife.
"Pamela took the knife from Micah and told Micah that he had just killed his son," Sadler wrote.
The first officer on the scene found Harrison with blood on his hands, the affidavit said.
Pamela Harrison told officers her son had driven from Alabama with Micah and two daughters, ages 4 and 5, on Tuesday. The children's mother did not accompany them.