Traffic policeman Wayan Sudarsa was found dead last week with wounds to his head and neck on a popular beach in the south of the Indonesian resort island.
Briton David Taylor and his Australian girlfriend Sara Connor were arrested and have been named as suspects, a step in the Indonesian legal system meaning investigators believe they have enough evidence to consider filing charges.
Taylor, a DJ, admitted in questioning yesterday to having a fight with Sudarsa on the beach after accusing him of stealing Connor's bag. He hit the officer with bottles, binoculars and a phone after being pushed, according to his defence lawyer.
Taylor got "mad" and they started to fight on the beach, with the Briton repeatedly hitting the policeman's head with a bottle until it broke, Purnomo said.
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"David was hitting violently, in a rage, with the bottle," said the police chief.
Connor, a mother from New South Wales, has maintained her innocence, saying she only sought to separate the fighting men.
A day after the policeman's body was found, the couple checked out of their hotel and burned their clothes, the police chief said.
They had initially tried to deny any confrontation with Sudarsa and had offered a series of confusing and contradictory accounts of what had happened, he said.
They could face up to 15 years in jail if found guilty of murder.
Bali, a pocket of Hinduism in Muslim-majority Indonesia, is a popular tourist destination known for its tropical climate and palm-fringed beaches.
Petty crime is common but murders are rare.