Murder carries the maximum penalty of 15 years in prison, while torture resulting in death carries a potential seven-year jail term.
One of the suspects was detained while he was about to leave the international airport in the Indonesian capital Jakarta and flown back to Bali, in co-operation with immigration and national police officials, he said.
“The other two already fled and were successfully returned because of the co-ordination between Interpol countries in the Southeast Asia region,” he said, without specifying the countries involved.
He did not disclose the alleged role of the third suspect, despite the search initially focusing on two suspects.
Bali police also showed several pieces of evidence to the media on Wednesday, including a hammer, pieces of clothing and bullet casings.
Witnesses, including Radmanovic’s wife, said the perpetrators who fled the scene after the attack were speaking in English with a thick Australian accent, according to a local police statement.
The Australian embassy in Jakarta directed questions to the Department of Foreign Affairs and Trade, which did not immediately respond to an AFP comment request.
Gun crime on the island of Bali and wider Indonesia is rare, and the archipelago nation has strict laws for illegal gun possession.
– Agence France-Presse