"Our wish is that it continues that way", Avicii's family added.
Bergling checked into a hotel in the Omani capital on Friday evening, hours after the star was found dead.
They have found "nothing suspicious", but the exact cause of death is yet to be confirmed. In 2014, he had his gallbladder and appendix removed.
Avicii was an global pop star, performing his well-known electronic dance songs around the world for die-hard fans, sometimes hundreds of thousands at music festivals, where he was the headline act.
Rock "n" roll had Buddy Holly, the psychedelic era had Jimi Hendrix and Janis Joplin and grunge had Kurt Cobain.
'These nights will never die, ' said Avicii before fading into darkness.
On Saturday, crowds in Stockholm attended a memorial dance party to pay tribute to Avicii. In a statement on his website past year, the musician said he had begun work on another release. The album came in top 10 in more than 15 countries.
Avicii collaborated with high-profile acts, producing Madonna's Devil Pray and the Coldplay hits A Sky Full of Stars and Hymn for the Weekend.
Radio stations around the world put his tracks such as his 2013 crossover hit "Wake Me Up" on heavy rotation and his singles and albums will find their way back onto the charts this week.
"Since it got so big in America the past couple of years, dance music is taking over everywhere", Avicii told the London Evening Standard. Calvin Harris, Zedd and other members of the EDM community expressed via Twitter their sorrow over the "Wake Me Up" hitmaker's passing. Just last week I was chatting with you and Shaun Duvet about working together, excited about being inspired by your recent visit in South Africa.
Avicii, born Tim Bergling, had been chilling with friends and kitesurfing.
There is apparently no reason at all to suspect any foul play based on the 2 autopsies that were performed on the body. It left fans around the world confused as to how such a bright light could be extinguished so early.
- Smart money points to Trump charge
- James Harden makes worrying claim, talks Houston Rockets title chances
- Keys to a Columbus Blue Jackets Comeback in Games 6 and 7
- Bucks even up series against Boston behind 27 points from Giannis Antetokounmpo
- Verdict on Asaram: Security beefed up in Rajasthan, Gujarat and Haryana
- Waffle House shooting suspect asks for lawyer as he's arrested
- Rob Gronkowski confirms he will play next season
- API reports surprise rise in United States oil inventories
- Veteran receives world's first total penis and scrotum transplant at Johns Hopkins
- Kanye West Supports Donald Trump with 'Make America Great Again' Hat