Asylum-seekers trying to reach Australia claimed Wednesday that members of the Australian navy subjected them to verbal and physical mistreatment as their boat was towed back to Indonesia.

One of the migrants, Yousif Ibrahim from Sudan, said they were handcuffed, called insulting names, and one was beaten with shoes before and during their voyage back to Indonesia where they arrived Monday.

The 28-year-old also said four people were left with burn marks on their hands when they were forced to hold on to a hot pipe on their boat as punishment for wanting to go to the toilet.

"We asked for water, they didn't want to give us. They called us inhuman words, like illegal refugees, monkeys from Africa," he told AFP, adding that two sick children were denied medicine.

Another asylum-seeker speaking to local media made similar claims. Australian Immigration Minister Scott Morrison refused to comment on the claims but insisted that Australian personnel act with the "highest levels of professionalism".

Ibrahim was among 45 immigrants, mostly from Somalia and Sudan, who set off from Indonesia, a major transit point for would-be refugees, to make the treacherous sea crossing to Australia last month.

But they were picked up on an island in Australian waters by crews from three Australian navy vessels and towed back to Indonesian waters, he said, as part of Canberra's tough border protection policies.

It was the first reported instance that the Australian navy has turned a boat back without informing Indonesian authorities, and prompted fresh anger in Jakarta at Canberra's policies.

Tensions were already running high between the neighbours after a diplomatic row erupted in November over claims Australian spies tried to tap the phones of Indonesian President Susilo Bambang Yudhoyono, his wife and ministers.

The row prompted Jakarta to freeze cooperation with Canberra in a number of areas, including people-smuggling.

In this week's incident, Ibrahim said the asylum-seeker boat landed on the remote island after four of the migrants were swept overseas on New Year's Day in rough seas.

However, they quickly found themselves surrounded by Australian navy personnel.

"They told us to go back to the boat, we refused. Then they used violence against us. One tried to run but they beat him with shoes," he said, speaking from a hotel at Kupang in eastern Indonesia, where the migrants are being housed while their cases are processed.

"They have pistols and weapons. We are afraid."

He said the migrants were handcuffed and taken back to the boat. They were released from the cuffs on the boat and then towed for four days towards Indonesia before the Australians left. They arrived on their own at Rote Island in eastern Indonesia on Monday.

Hidayat, a senior police officer from the Rote Island area who goes by one name, said one migrant had complained he was forced to hold part of a hot engine.

"It is true that he has a blister on his hand," he said.

Somali migrant Marke Abdulah Ahmad, who was on the boat, also told Indonesian news website Tempo the asylum-seekers were subject to abuse.

Morrison refused to comment on the reports in line with his conservative government's decision not to discuss "on-water" activities.

But he added: "All personnel involved in border protection operations... conduct their roles with the highest levels of professionalism, integrity and personal courage in extremely trying and challenging circumstances."

He added any actions taken were consistent with Australian domestic law and its obligations under international law.

The tough policies aimed at stemming the flow of asylum boats arriving in Australia were a key part of new Prime Minister Tony Abbott's election campaign in September.

Hundreds of people have died trying to make the sea crossing to Australia in recent years.