"He was like my brother," Pop's statement read of Scott. "He and Ron have left a huge legacy to the world. The Ashetons have always been and continue to be a second family to me. My thoughts are with his sister Kathy, his wife Liz and his daughter Leanna, who was the light of his life."
Asheton suffered from undisclosed illnesses in 2011 and was unable to perform at summer music festivals in Europe with the Stooges.
"He was on a flight to England when all sorts of hell broke loose," Pop told Rolling Stone in 2011. "Without proper medical attention right there he would have bought it. He got very, very good care from the British and all sorts of tests."
While the Stooges weren't a commercial success, they went on to become one of the significant bands in punk music. Their raw sound helped inspire the first generation of punk musicians. The band influenced acts from Patti Smith to the Ramones to Sid Vicious. The group landed in the Rock and Roll Hall of Fame in 2010.
After recording three albums in the late 1960s and early 1970s, the Stooges split and Pop went on to a successful solo career. The band reunited for 2007's "The Weirdness" and "Ready to Die," released last year.
"It warms my heart to read how much he has inspired and the love and respect so many have for him and his music," Leanna Asheton said in an email to The Associated Press late Monday.
She remembered her father not only for his love of playing and listening to music, but for his humor and charm. She said they enjoyed going to gigs together in recent years, including Black Rebel Motorcycle Club in Detroit, which she said was his favorite and last show.
Always rooting for the underdog, he also was a fan of poet and writer Charles Bukowski. His daughter said her father's favorite Bukowski quote was, "What matters most is how well you walk through the fire."
Asheton was born on Aug. 16, 1949, in Washington, D.C. He played drums for other bands, including Sonic's Rendezvous Band, the group led by former MC5 guitarist Fred "Sonic" Smith. Along with his wife and daughter, Ashton is survived by his stepsons Simon and Aaron, whom "he loved as his own," his daughter said.
Associated Press writer Jeff Karoub contributed to this report from Detroit.