Nashville police said an argument broke out between the two friends before Oteri, 69, was killed with a pocketknife, The Tennessean, a Nashville newspaper, reported Tuesday.
Fagan, 61, was been charged with criminal homicide and held without bond.
Investigators were piecing together details of the fight between country songwriter Fagan and his longtime friend, roommate and business associate Oteri, the newspaper report said.
Police said Fagan told investigators the stabbing occurred Saturday night after the two had been drinking and arguing. Fagan may not have known the knife wounds to Oteri's wrist were fatal, police spokesman Don Aaron said.
"Mr. Fagan had asked a friend to go by and check on Mr. Oteri," Aaron told The Tennessean. "There was no indication Mr. Fagan had any idea that Mr. Oteri was dead."
Fagan had success as a songwriter, with songs recorded by artists such as Neil Diamond, Shania Twain and Hank Williams Jr. Fagan also wrote No. 1 hit songs "Be My Baby Tonight" and "Sold (The Grundy County Auction Incident)" for John Michael Montgomery.
Oteri was the father of Cheri Oteri of NBC's "Saturday Night Live."