Calls are growing for an inquiry into reports that Australian officials paid people-smugglers bound for Australia thousands of dollars to turn their boat back to Indonesia.

Indonesia and the United Nations have also expressed serious concern.

A boat captain and two crew members arrested on suspicion of human trafficking told Indonesian police that Australian authorities had paid each of them A$5,000 (€3,400) to turn back their vessel with 65 migrants on board.

The passengers, including children and a pregnant woman, were from Bangladesh, Sri Lanka and Burma, (also known as Myanmar).

Australia has vowed to stop asylum-seekers reaching its shores, turning boats back to Indonesia when it can and sending asylum-seekers for long-term detention in camps in impoverished South Pacific nations Papua New Guinea and Nauru.

Australian Foreign Minister Julie Bishop and Immigration Minister Peter Dutton last week denied reports of payment to the smugglers.

However, both declined to repeat the denials during a heated parliamentary debate today.

Prime Minister Tony Abbott has also declined to comment, citing operational security.

A growing chorus of opposition politicians wants the government to explain.

Opposition Labor Party leader Bill Shorten said the refusal to dispel the reports would entice people smugglers.

"By failing to deny reports that criminal people smugglers could be paid $30,000 if they make it to an Australian vessel, isn't the government providing a cash incentive for these dangerous voyages to take place?" Mr Shorten asked Mr Abbott.

Greens Party Senator Sarah Hanson-Young said she had asked the Australian Federal Police to investigate.

Labor has sought an inquiry from the country's auditor-general.

There are signs the allegations are already straining ties between uneasy neighbours Australia and Indonesia, which are only just beginning to improve after Indonesia's execution of two Australians on drugs charges this year.

Over the weekend, Indonesian foreign ministry spokesman Arrmanatha Nasir said Australia would have stooped to a "new low" if the reports were true.

The UN and human rights groups have criticised Australia over its tough asylum-seeker policy.

Payments to criminals were unacceptable, said United Nations High Commissioner for Refugees (UNHCR) Antonio Guterres.

"We need to crack down on smuggling and trafficking, not paying them, but putting them in jail whenever possible, or prosecuting them," he told the BBC.