Prime Minister Tony Abbott has declared Australia will pursue the crackdown on boats carrying asylum-seekers into its waters, saying Indonesia should understand it is a matter of sovereignty.

Jakarta has reacted furiously to repeated incursions by Australian vessels into Indonesian waters, reportedly while attempting to turn back boats carrying would-be refugees, despite an official apology from Canberra.

Speaking from Switzerland on Tuesday, Abbott said the relationship with Indonesia was, broadly speaking, his country's most important single one and President Susilo Bambang Yudhoyono was "a very good friend of Australia".

"All of that said, for us, stopping the boats is a matter of sovereignty and President Yudhoyono of all people ought to understand, does understand, just how seriously countries take their sovereignty," he told reporters in Davos.

"So we will continue to do what we are entitled to do to secure our borders."

After winning elections in September, Abbott's conservative government launched Operation Sovereign Borders which aims to stop people-smugglers, who often operate out of Indonesia, from bringing asylum-seekers to Australia by sea.

Arrival numbers have since dropped dramatically, but the policy which includes turning back boats when it is safe to do so has been received coolly by Jakarta and criticised by refugee advocates.

Australia says the incursions were inadvertent but reports have suggested the warships might have known they strayed into foreign waters, a suggestion backed Wednesday by a retired Indonesian general.

"I studied in Australia -- in the military academy. The Australian navy doesn't have wooden boats, they have warships equipped with modern technology," Tubagus Hasanuddin told the Australian Broadcasting Corporation.

"They should have known which part of the water is Indonesia and which is not."

The Australian navy has also been accused of mistreating asylum-seekers onboard a vessel which was pushed back to Indonesia, with the ABC saying they claimed to have been beaten and burnt.

The government has denied the claims, but the ABC reported that Indonesian police had said 10 asylum-seekers required medical treatment, including seven who had burns on their hands from holding onto a hot pipe on their ship's engine.

The incursions have come as ties between the nations have been strained by a spying row triggered by reports that Australian spies tried to tap the phones of Yudhoyono, his wife and several top officials in 2009.