Torrence began his career competing for the United States, and held the national record for the indoor 1000m, which he set in 2014 and still stands.
According to the police statement, there were no obvious signs of foul play, BBC reported.
A native of California, Torrence won silver for the U.S. at the World Relay Championships in 2014 and finished second at the Pan American Games in 2015.
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On Twitter, USA Track and Field described the news as "devastating", New Zealand's double Olympic medallist Nick Willis wrote that "nobody was more dedicated to their running" than Torrence and Canada's three-time Olympian Nate Brannen said his friend will be "greatly missed".
David Torrence, 31, came to Scottsdale a few weeks ago to train.
The organisers of next week's Hoka One One Long Island Mile, a race Torrence won in 2015 and 2016, have said they will rename it in his honour. "He was going for #3 this year", Merber tweeted.
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Torrence, who was born in Japan and grew up in California, became a standout runner at Cal-Berkeley, and parlayed that into a successful pro career competing both for the USA and then Peru.
Fellow athletes paid tributes to Torrence. In October of that year, 'after a night of trash talking and pasta, ' David made a bet with a teammate: "he would run a sub-4:00 mile by the end of the year; if he was successful, his teammate would have to run a naked mile".
One of the top middle- and long-distance runners in the world passed away on Monday. "He got 100% out of himself every day".
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