In a statement (via Billboard), Bergling’s family say they would like to thank fans “for the support and the loving words about our son and brother”.
“We are so grateful for everyone who loved Tim’s music and have precious memories of his songs,” they say.
“Thank you for all the initiatives taken to honor Tim, with public gatherings, church bells ringing out his music, tributes at Coachella and moments of silence around the world.
“We are grateful for the privacy during this difficult time. Our wish is that it continues that way.”
The statement from Bergling’s family comes after the likes of Alison Wonderland, A State Of Trance Festival and Bergling’s ex-girlfriend paid tribute to the late DJ, who died in Muscat, Oman on Friday.
Two autopsies carried out on Bergling’s body have reportedly led authorities to believe there is “no criminal suspicion in the death”.
Neil Jacobson, president of Avicii’s label Geffen Records, earlier told Variety that Bergling was writing “his best music in years”, and was working on an album at the time of his death.
“We had to actually put end times on the sessions because Tim would just work for 16 hours straight, which was his nature,” he said.
“You had to pull him out. Like, ‘Tim, come on. Go to bed. Get some rest.’… It’s just a tragedy. We have this incredible, magical music.”
Avicii’s final album Stories was released in 2015. He last toured Australia in 2013 as part of Future Music Festival, and was taken to hospital in Brisbane during that time.