Indonesian police have arrested three Australian men over a shooting that killed a fourth at a villa on the resort island of Bali, its police chief says.

The three suspects detained on Tuesday were accused of having “prepared and executed” the shooting, Bali police chief Daniel Adityajaya said.

“We have arrested three suspects,” he said.

The men have been charged with premeditated murder and could face the death penalty if the charges are proved.

Police declined to identify the men, however, referring to them only by the initials C, D and T.

Saturday’s shooting at Villa Casa Santisya near Munggu Beach in the district of Badung, north of the tourist hub of Kuta, just after midnight killed Zivan Radmanovic, 32 and seriously wounded a fifth Australian, Sanar Ghanim, 35.

Radmanovic’s wife, 30-year-old Gourdeas Jazmyn, woke to her husband’s screams shortly before midnight. She cowered under a blanket when she heard multiple gunshots.

Jazmyn later found her husband’s body and the injured Ghanim, whose wife has also testified to seeing the attackers.

Ghanim was taken to hospital after being beaten and shot multiple times. Balinese media reports he has since been released “under the supervision and handling of the national police”, and is considered a witness in the case.

Radmanovic was shot in a bathroom, where police found 17 bullet casings and two intact bullets.

Indonesian authorities previously said they had arrested two people for the shooting, one at Soekarno-Hatta airport near the capital, Jakarta, as he prepared to leave the country.

“We arrested him just before he managed to leave,” Adityajaya said on Wednesday.

The other two were detained abroad after police sought the co-operation of Interpol in South-East Asia, they said. They declined to say where the arrests were made.

They also seized items such as a nine-millimetre gun, a motorcycle and two cars the suspects had used to flee the scene of the crime, Adityajaya said.

Police have not given a motive for the crime, saying their investigation continues. Adityajaya said a further suspect could be identified as the plot’s mastermind.

-with AAP