Indonesia has warned Australia not to expect to continue to offload asylum seekers on its shores after appearing to refuse to accept a large group of refugees rescued off the south coast of Java.

If confirmed, the decision to reject Australia's request to disembark the group of about 63 asylum seekers effectively means Indonesia now has its own version of the Abbott government's turn-back plan.

The asylum seekers remained aboard a Customs vessel off the coast of Java on Friday.

Indonesian Foreign Minister Marty Natalegawa, while refusing to comment specifically on the boat which was the subject of a rescue operation on Thursday, foreshadowed that Jakarta would no longer take back asylum seekers unless they were in imminent danger.

"The question is under what circumstance are we bringing them to Indonesia. There wouldn't be any apparent need for them to be brought back to Indonesia," Dr Natalegawa said on Friday.

Despite the development, Immigration Minister Scott Morrison at his weekly briefing earlier denied there was a stand-off between Indonesian and Australian authorities.

"What's important is the people who are the subject of our assistance are all accounted for," Mr Morrison said.

He said he wasn't in the business of offering "micro details" on military matters.

The commander of Operation Sovereign Borders, Lieutenant-General Angus Campbell, also refused to provide details about the stand-off.

"I will not comment further in relation to on-water matters," General Campbell said three times, after reporters repeatedly questioned him on the matter.

Prime Minister Tony Abbott defended the government's reluctance to offer details of operations at sea, saying the important thing was to stop the boats.

"The best way to stop the boats is to ensure ... we are not providing a shipping news service for people smugglers," he told reporters in Melbourne.

But Indonesian officials on Friday morning were continuing to resist appeals from Australian authorities to offload the asylum seekers at a port in Java.

A spokesman for Djoko Suyanto, the Indonesian co-ordinating minister for Legal, Political and Security Affairs, said Jakarta was reluctant to accept them because the boat had been in working order when first approached by the Australian navy vessel HMAS Ballarat.

"From what I've been told, the boat was fine and they were not in danger. If that's the case, then we reject it," Agus Barnas told AAP on Friday.

"We don't want Indonesia to be a dumping ground, but we don't want Australia to accuse us of not doing anything. We want to respect Australia.

"At least for the time being we will not accept them."

The fact that Mr Djoko's office was so heavily involved, instead of the national search and rescue agency BASARNAS, also suggests Indonesia was treating the matter as more than simply operational, and that political considerations were playing a part.

The stand-off comes amid rising tensions between Canberra and Jakarta over the spying row that has threatened to derail cooperation in various areas, including people smuggling.

Foreign Minister Julie Bishop on Friday attempted to play down suggestions of a rift, but also refused to provide details of the unfolding drama off Java.

The boat had been bound for Australia when it issued a distress call about 5.30am on Thursday morning.

General Campbell confirmed the vessel first called for help about 43 nautical miles south of Java, inside Indonesia's search and rescue zone.