The sheriff of the Minnesota county where the iconic musician had his home made the statement after a post-mortem examination.
There was no sign of trauma on the body, Sheriff Jim Olson said, suggesting Prince had died alone.
Prince Nelson Rogers, 57, was found dead in a lift on his Paisley Park estate on April 21.
Fans have been wearing purple, the color associated with the musician who sold more than 100 million records.
Prince’s innovative music spanned rock, funk and jazz. He was at his peak in the 1980s with albums like Dirty Mind, 1999 and Sign O’ The Times.
Sheriff Jim Olson warned that full results from the post-mortem could take several weeks, and the incident was still under investigation.
He said it was not unusual for there to be no one in the residence except Prince.
Prince was last seen at about 20:00 on April 20 and was found unconscious by some of his staff at about 09:30 the next morning.
He had been rushed to hospital in Illinois six days earlier, while flying home from a concert in Georgia, but was treated and released a few hours later.
Quoting unnamed sources, TMZ reports that Prince was treated in Illinois for an overdose of the painkiller drug Percocet.
Declining to give details of the preliminary findings, medical examiner spokesperson Martha Weaver said a full set of tests would be done on the body, involving tissue and blood samples.
Earlier, she announced that the body would be released to the family on April 22.
Sheriff Jim Olson confirmed police were in contact with Prince’s family.
“We have no reason to believe at this point that this was a suicide,” he said, then added, “but again, this is early on in the investigation and we’re continuing to investigate.”
The sheriff spoke of Prince as a good member of the community and said he had been a “friend to [his staff] as well as being an employer”.
Fans have set up impromptu memorials in Prince’s home town Minneapolis and in New York.
Prince had spoken about struggling with childhood epilepsy, the Associated Press reports, and friends say he had hip trouble.
His former percussionist, Sheila E, told the news agency Prince had suffered the effects of years of jumping off risers and speakers on stage while wearing high heels.
Prince’s latest album, HITnRUN Phase Two, was released in 2015 and he had been touring as recently as last week.
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