There is no indication that Prince took his own life, Carver County Sheriff Jim Olson said.
Sheriff Olson added that there were no obvious signs of trauma on the singer's body.
However, police are investigating whether the singer's death involved foul play.
Speaking at a press conference at Carver County Courthouse in Chaska, Minnesota, Sheriff Olson refused to comment on reports that Prince had consumed a powerful painkiller before his death.
He said Prince was last seen at 8pm the night before his death when he was dropped off at his Paisley Park estate.
The singer had been alone at the estate and staff member had been unable to reach him, Sheriff Olson added.
A spokeswoman for the Midwest Medical Examiner's Office said it would not release information from the post-mortem examination until "all results are obtained", and added that the findings of a toxicology scan "could likely take weeks".
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Authorities in the US state of Ohio are investigating shootings with 'multiple fatalities' in the town of Peebles, in Pike County, approximately 65 miles east of Cincinnati.
According to NBC News affiliate, WLWT, officers were dispatched to the small town at around 8:21am local time.
There are unconfirmed reports that at least seven people have been killed.
"I cannot confirm seven dead, I can only confirm multiple deceased," Jill Del Greco, public information officer for Attorney General Mike DeWine, told NBC.
She added that she was unaware of any arrests.
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Barack Obama has paid tribute to Prince, saying the world has lost a "creative icon" and an "electrifying performer".
The White House issued the following statement:
Today, the world lost a creative icon. Michelle and I join millions of fans from around the world in mourning the sudden death of Prince.
Few artists have influenced the sound and trajectory of popular music more distinctly, or touched quite so many people with their talent.
As one of the most gifted and prolific musicians of our time, Prince did it all. Funk. R&B. Rock and roll. He was a virtuoso instrumentalist, a brilliant bandleader, and an electrifying performer.
“A strong spirit transcends rules,” Prince once said - and nobody's spirit was stronger, bolder, or more creative. Our thoughts and prayers are with his family, his band, and all who loved him.
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