Indonesian police have told the ABC that a second boat carrying asylum seekers has been forced back to Indonesian waters by the Australian Navy.

The first boat was found shortly before Christmas on an island called Rote in Indonesia's East Nusa Tenggara region.

It allegedly had been "pushed" or forced back into Indonesian waters by the Australian Navy.

The 47 asylum seekers on board have told authorities they were adrift after running out of fuel, before running aground on the island about six days later.

A second boat carrying 45 asylum seekers has now been found on the same island.

Local police Chief Hidayat says group also claims their boat was pushed back by the Australian Navy.

Indonesia's foreign minister, Marty Natalegawa, has again reiterated his country's opposition to any move by Australia to turn asylum seeker boats around.

"Let me just once again put on record our rejection of [policies] that resemble the pushing back the boat," he said.

"Such policy is not actually conducive to a comprehensive solution to the issue."

Dr Natalegawa has previously raised his concerns with Foreign Minister Julie Bishop, who told him Australia would press ahead with the policy.

The recent news is likely to further strain relations between Australia and Indonesia, which have been tense since revelations of a spying scandal came to light late last year.

Dr Natalegawa says he is in almost daily contact with Ms Bishop, as Australia and Indonesia work to restore relations.

"It's not something that can be simply restored willy-nilly by the adoption of certain declaration or agreement. What's needed is gradual process of restoration of confidence or trust and this is where we are just now," he said.

News of the first alleged turn back was only recently reported in local Indonesian news, after refugee rights activists noticed reports and posted them on Twitter.

Local police chief Hidayat says the asylum seekers had been on a boat trying to get to the Ashmore Islands.

He says the group left South Sulawesi bound for Australia on December 8.

They were then intercepted on December 13 by the Australian Navy and "pushed" back to Indonesian waters.

On December 19, they were found on Rote Island, where Indonesian authorities picked them up.

Immigration Minister Scott Morrison has released a statement in relation to reports surrounding the first boat.

The statement says the Government will not comment on the reports.

"For operational security reasons, the Government does not disclose, confirm or otherwise comment on reports of on-water activities in relation to Operation Sovereign Borders," the statement said.

"Australia respects Indonesia's territorial sovereignty and will continue to do so, just as Indonesia has stated it respects Australia's territorial sovereignty.

"It is not the policy or practice of the Australian Government to violate Indonesian territorial sovereignty. Any suggestion to the contrary is false."

Labor, Greens call for answers on boat turn-backs

Labor and the Greens say the Government must reveal the details of the alleged incident.

"We've got a situation where a boat has been towed back by Australian officers, the boat has run aground. These people could have drowned," Greens Senator Sarah Hanson-Young said.

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

The Federal Government has previously outlined its intention to "turn back" boats "where it is safe to do so" as part of its asylum seeker policy.

Under Operation Sovereign Borders, Mr Morrison had been providing information about what it calls "on-water operations" during a weekly briefing given each Friday.

Mr Morrison has in the past refused to release more information about asylum seeker operations because of "national security" and "the protection of public safety".

He gave his last weekly briefing in December and it is unclear whether they will continue this year, with reports a weekly email may be distributed instead.