Indonesia has again warned the federal government against asylum-seeker turnbacks following reports the Australian Navy secretly turned around at least one boat in recent weeks.

Reports from Indonesia and Australia say an Ashmore Island-bound boat was turned back either in December or on Monday - or possibly on both occasions - and subsequently became stranded on Rote Island, near West Timor.

The Indonesian reports quoted local police, while Fairfax Media cited unnamed Australian Defence sources and the Indonesian water police.

Immigration Minister Scott Morrison would not comment on the conflicting reports for "operational security reasons", despite the coalition having a pre-election policy to turn boats back when safe.

Indonesian Foreign Minister Marty Natalegawa also refused to comment on the specifics when asked about the reports on Tuesday.

"But as a policy, I shall repeat this once again: Indonesia rejects and is against the policy of boat turnbacks because it's not a solution," he told reporters in Jakarta, speaking in Indonesian.

Agus Barnas, a spokesman for Indonesia's Coordinating Ministry for Politics, Law and Security - which has responsibility for people smuggling - said he was unaware of any turnbacks.

He said Indonesia was still observing a moratorium on co-operating with Australia on people-smuggling after last year's spying scandal.

"So far, there's no policy that the co-operation would resume," Mr Barnas said.

"The talk on forming a code of conduct is still in process."

Speculation about possible boat turnbacks follows a stand-off in November when Australia tried to force a vessel back into Indonesian waters.

The Abbott government backed down after Indonesia refused to accept the asylum seekers, who were eventually transferred to Christmas Island.

Mr Morrison says that Australia respects Indonesia's territorial sovereignty "and will continue to do so".

"It is not the policy or practice of the Australian government to violate Indonesian territorial sovereignty," he said in a statement on Tuesday.

Dr Natalegawa said Indonesia's relationship with Australia was still in a "difficult phase" in the wake of the spying revelations.

But he said he was in daily contact with Foreign Minister Julie Bishop in an effort to repair the damage.

"What's needed is a gradual process of restoration of confidence or trust, and this is where we are just now," he said.

The Greens want Mr Morrison to provide details of any turnback operation, saying the lives of asylum seekers could have been endangered.

"These people could have drowned," Senator Sarah Hanson-Young said.

"How many other boats has this occurred to that we've never heard about?"