"We have not found anything that could explain what happened. We do not know," police spokesman Lars Byström told the AFP news agency.
Early on Saturday morning, the car, which one witness said was travelling at around 70 kilometres (40 miles) per hour, drove through a signal light and two barriers towards a canal bridge near Stockholm which initial reports suggested had not fully shut after letting a vessel pass underneath.
However, authorities later confirmed that the bridge was in fact in the process of opening for the ship.
The four band members and their manager, aged between 20 and 35, died when the car crashed 26 metres into the water.
Truck driver Jonny Alexandersson told the Aftonbladet newspaper that other vehicles were waiting for the bridge to open and close fully, but the band's car sped towards the bridge "at a crazy speed".
Swedish police and bridge operators said that the barriers and signal lights were working property at the time of the crash.
Echoing comments police made to The Local on Monday, Byström said: "For the moment we are examining the car, to see if everything functioned properly, including the brakes, and we are examining the bodies of the people that were inside."
The band, who last year released a debut single, had been in Sweden for a Friday night 'Where's the Music' festival in the central city of Norrköping and was heading back to Britain for a gig the following day.
Festival organizers paid tribute to the group, telling The Local on Tuesday: "Viola Beach was a brilliant band, and we truly are heartbroken."
Meanwhile, Swedish broadcaster SVT revealed that crew onboard an oil tanker on its way to Södertälje on Saturday had seen the car fall but believed it was chunks of snow dropping from the bridge.
After contacting Sweden's maritime authority (Sjöfartsverket), which was not yet aware of the accident at the time, they received permission to carry on and ended up sailing right above the wreckage.
The Swedish Accident Investigation Authority, the top national agency in charge of heading inquiries on fatal accidents, said on Tuesday that it was considering opening a probe into the crash.
"The information we have seen does not indicate that there was anything wrong with the bridge, but we've only seen that information in the media. So now we're going to get the basic facts so that we can decide whether to go ahead or not," spokesperson Johan Gustafsson told SVT.