Prime Minister Tony Abbott denies Indonesia is calling the shots on asylum seekers after it directly contradicted the Federal Government over a boat picked up last week.

A standoff between Canberra and Jakarta developed after a boatload of about 60 asylum seekers was rescued by an Australian ship off the south coast of Java.

Australian authorities wanted Indonesia to take back the asylum seekers, but the request was refused and the group was taken to Christmas Island for detention.

Key points: 60 asylum seekers rescued off Java coast last week

60 asylum seekers rescued off Java coast last week Taken to Christmas Island after Indonesia refused to take them back

Taken to Christmas Island after Indonesia refused to take them back Scott Morrison said it was not a "turn-back" situation, which Basarnas disputes

Scott Morrison said it was not a "turn-back" situation, which Basarnas disputes Tony Abbott denies Australia is continuously buckling to Indonesia on asylum seekers

Tony Abbott denies Australia is continuously buckling to Indonesia on asylum seekers Government confirms another boat has sunk off Java coast

Immigration Minister Scott Morrison said it was not a situation of turning the boat back but Indonesia's rescue agency Basarnas has disputed that, saying Australian authorities either towed or escorted the boat nearly 50 nautical miles back towards Indonesia.

Mr Abbott has refused to confirm or deny Indonesia's version of events.

"I'm just not going to comment on operational matters," he said in his first interview with 7.30 as PM.

He denied Australia is continuously buckling to Indonesia over asylum seekers.

"I'm not interested in a testosterone contest, I'm interested in stopping the boats," he said.

"I'm not going to used loaded language myself, I'm not going to run around beating my hairy chest and saying that I've out-stared someone and I'm not going to say that someone has out-stared me either.

"This is not a question of two countries trying to prove who's the toughest with each other.

"It's a question of two good friends working together, which is clearly in the best interests of both of our countries."

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Mr Abbott denied he was furious with Indonesia for releasing operational details when the Coalition prefers to do it via a weekly briefing.

"In the end all I can absolutely control is how my Government responds and what I've said with the Indonesians is we're not going to conduct dialog through the media," he said.

"If we've got something to say to the Indonesians, we'll say it to them up front, honestly, face to face.

"I'm not in the business of lecturing people, I'm in the business of being an honest, frank, candid trustworthy partner.

"I want to stop the boats for Australia's sake and the sake of common humanity.

"Surely all Australians, including the media, should want to stop the boats, not to provoke an argument."

Basarnas's head of evaluations, Yopi Haryadi, says the boat was intercepted by Australian authorities 107 nautical miles from Indonesia, or about half way to Christmas Island.

It was then taken by Australian authorities to a location about 58 nautical miles off the coast as Australia attempted to get Indonesia to accept its return.

Mr Morrison released a statement this evening saying the incident was a search-and-rescue operation and not a turn-back operation, adding that the initial contact was 43 nautical miles south of Java.

He added Australian authorities tried to take rescued people to the closest place of safety, which was Indonesia.

"Australian authorities conducted the rescue and ensured the safety of all on board," Mr Morrison said.

"The closest place of safety from the place of rescue was in Indonesia and a request was made, as previously advised, for passengers to be transferred at sea to Indonesian authorities, consistent with international search and rescue protocols."

Basarnas has now indicated a change in policy in direct response to the Australian Government's attempt to return asylum seekers.

Mr Haryadi says the country's coordinating ministry of politics, law and security has taken control of decisions around whether Australian Customs and Navy ships can enter Indonesian territory.

It is aimed at stopping Australia returning asylum seekers.

The minister responsible, Djoko Suyanto, says Indonesia has never agreed to Australia's wishes and that will not change.

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Another asylum boat breaks down off Java coast

Meanwhile, Indonesian authorities say they've rescued 51 asylum seekers from their stricken vessel off the south coast of west Java.

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The boat suffered engine failure about five kilometres off Manuk beach in Banten province on Wednesday morning, Indonesia's search and rescue agency said.

With the help of local fishermen, nine people including five children were brought back to land, agency spokesman Mochamad Hernanto said.

The rest of the asylum seekers initially refused help, but eventually gave in and were helped ashore.

Indonesia's rescue agency, Basarnas, says the asylum seekers were from Sri Lanka, Bangladesh and Sudan.

Mr Morrison said Australian authorities were not involved in the rescue, which was coordinated by Indonesian authorities.