The prime minister, Tony Abbott, has defended his government's secret handling of asylum seekers amid allegations of brutal treatment by the navy.

Abbott said his "closed book" approach to border operations was aimed at preventing the issue becoming "sport for public discussion".

He refused to comment on reports that the navy had towed boats back to Indonesia, a practice that he appeared to rule out in October. Speaking in a radio interview he said: "The point is to stop the boats."

He added: "I'm pleased to say it is now several weeks since we've had a boat, and the less we talk about operational details on the water the better when it comes to stopping the boats."

Prior to the federal election Labor had provided a detailed breakdown of asylum arrivals and boat-related incidents. Abbott's government, by contrast, has limited information to a weekly press briefing while officials have refused to answer questions about incidents, claiming this could jeopardise operations.

Asylum seekers have claimed that members of the Australian navy verbally and physically mistreated them as their boat was being towed back, after being intercepted at an island near Darwin.

General David Hurley, the chief of the Australian Defence Force (ADF), defended navy personnel against the accusations, which were aired by the ABC amid ongoing confusion over Australia's implementation of its hardline policies to deter asylum seekers.

Hurley said up to 800 ADF personnel assigned to the border protection focused Operation Resolute were "trained to operate with the highest degree of professionalism and integrity" and conducted themselves "in a humane and considerate manner".

His statement came after the ABC reported that two men who had said they were on asylum seeker boats towed back to Indonesia by the Australian navy said they were mistreated before being abandoned at sea.

The two men were said to be speaking from Kupang in Indonesia and said to have been on two different boats that were towed back. The ABC said the two stories were "difficult to verify" but "strikingly similar".

One man named Yusuf, identified as a Sudanese asylum seeker, told the ABC he and his wife had joined more than 40 people on a boat in Indonesia and reached a small island off the coast of Darwin before the engine broke down on New Year's Day. Two Australian naval ships, HMAS Parramatta and HMAS Glenelg, arrived on the scene.

Yusuf told the ABC the navy used force on some people, including women, while transferring them to one of the navy boats and restrained a number of people. Asylum seekers were wrongly told they were being taken to Australia's Christmas Island and given one meal a day during the five-day towback. The group was abandoned at night in rough seas off Indonesia's Rote Island, he told the ABC.

The second man, Marke, identified himself as Somali and was said to be on the first boat reportedly towed back to Indonesian territory on 10 December. He said personnel from HMAS Parramatta and HMAS Maitland had treated asylum seekers roughly and also said they were told they were heading towards Christmas Island.

"They told us a lie," Marke told the ABC. "When we reach, when we were nearby the island of Indonesia, they … fix one of our machines.

"They start our machine. They say: 'Go, you can land over there. It's about 15km.' And then they seemed to run away and disappeared."

But Hurley said that in his view Australia's navy, army and air force personnel had conducted themselves "in a humane and considerate manner that is a credit to them and to the Australian Defence Force".

"Defence Force personnel assigned to Operation Resolute are required to conduct operations in an unpredictable and demanding environment under intense scrutiny," Hurley said.

"They are trained to operate with the highest degree of professionalism and integrity and consistently demonstrate great compassion and courage, often at great risk to their own safety."

Hurley also asserted that defence operations were "consistent with Australian domestic law and Australia's obligations under international law".

He said up to 800 ADF personnel were assigned to Operation Resolute at sea, in the air and on land, "working alongside their colleagues from the Australian Customs and Border Protection Service (ACBPS) and other agencies to protect and maintain Australia's borders and maritime interests".

On Thursday afternoon the ACBPS issued its own statement backing Hurley's denial of the mistreatment claims.

"Allegations that illegal maritime arrivals have been treated inhumanely are false and inconsistent with the professionalism, culture and practices of any Australian government authority, including the Border Protection Command," said the service's acting chief executive, Roman Quaedvlieg.

Earlier, the Greens' spokeswoman on immigration, Sarah Hanson-Young, said she was concerned about the reports of asylum seekers being treated harshly during towback operations. Hanson-Young indicated she did not regard such incidents as the fault of the navy or customs but rather the "cruel" policies they were forced to implement.

"Tony Abbott is breeding a toxic culture of hate and fear," she said.

Labor's acting immigration spokesman, Mark Dreyfus, had earlier declined to comment on the claims of mistreatment, saying only that it reinforced the opposition's call for greater openness about asylum seeker operations.

"I'm not going to speculate because it's for the government to explain the circumstances. It's for the government to reassure Australians that everything that's been done does comply with international law, that everything that's been done complies with our obligations under the refugees convention," Dreyfus told the ABC.

Indonesian authorities have sent mixed messages over their willingness to co-operate with Australia's efforts to send asylum seeker boats back towards Indonesia. The commander of the Indonesian military, General Moeldoko, was reported in the Jakarta Post as saying he had spoken with Hurley who told him "that Indonesia should understand if Australia drove back undocumented migrants attempting to enter the country using Indonesian boats or if any Indonesians were found aboard".

"I have agreed. Therefore, we don't need to feel offended," Moeldoko said.

But other senior Indonesian officials have voiced their opposition to such actions.

The Jakarta Post quoted the Indonesian president's spokesman, Julian Aldrin Pasha, as saying that the president, Susilo Bambang Yudhoyono, had yet to discuss the conflicting statements over the issue: "I haven't heard the statements directly from the relevant officials so I don't know about them. Also, the president has yet to discuss the issue."

The ADF responded to media inquiries about the reported agreement with Moeldoko by pointing to a previous interview in which Hurley confirmed the two had discussed military co-operation on 18 December. During that interview, Hurley spoke of restoring the relationship. "General Moeldoko needs to do what his government directs him to do, but overall, we've been able to continue on very positively," Hurley told Sky News at the time.

Abbott promised before the election to turn around boats when safe to do so. Recent media reports stated that boats had been towed back towards Indonesia.

During a visit to Indonesia on 1 October, Abbott made clear that his policy was to turn boats around rather than actually tow them back: "Can I just scotch this idea that the coalition's policy is or ever has been towbacks? Our policy, which we have repeated till we are blue in the face, is that we reserve the right to turn boats around where it is safe to do so. There is a world of difference between turning boats around in Australian waters and the Australian navy towing them back to Indonesia."

The opposition leader, Bill Shorten, said on Thursday the government must answer legitimate questions about what boat policies it was actually implementing. "The government needs to stop hiding the truth and start answering the most basic questions," he said.

The Indonesian foreign minister, Marty Natalegawa, refused to comment on the specific incidents when asked about them 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.