Indonesia's vice president warned Monday that paying people-smugglers would amount to "bribery" after Australia was accused of handing out money to turn back a boatload of asylum-seekers.

Allegations that the captain and five crew of a boat, carrying migrants from Bangladesh, Myanmar and Sri Lanka, were each paid US$5,000 by an Australian immigration official to turn back to Indonesia were made to police on Rote island in the country's east last week.

Tensions between Jakarta and Canberra -- already high after the recent execution of two Australians in Indonesia -- are escalating after Prime Minister Tony Abbott refused to deny the allegations, prompting demands from Jakarta for an explanation.

Indonesia has previously expressed disapproval at the tough immigration policy implemented by Abbott's conservative coalition after it came to power in 2013. This includes turning back boats, mostly to Indonesia, when it is safe to do so.

Abbott is also under pressure at home, with the opposition Labor Party asking the auditor-general to investigate and the Greens party referring the matter to the police.

Indonesian Vice President Jusuf Kalla stepped up the pressure, saying that if such a payment had been made, it would be a "form of bribery".

"It is a mistake committed not only by the people who bribe others but also by the state. That act is against the code of ethics in state relations," he was quoted as saying by the state-run Antara news agency.

However he added that Indonesia wanted to confirm whether the allegations were true before taking any action.

Earlier Australian Foreign Minister Julie Bishop suggested that Indonesia was to blame for failing to properly manage its borders, prompting an angry response from her Indonesian counterpart Retno Marsudi.

Marsudi, who had demanded answers from Australia's ambassador about the issue at the weekend, accused Canberra of "diverting the issue", adding: "It isn't difficult for Australia to respond to my question... about the payment issue."

Indonesia 'committed to border control'

Foreign ministry spokesman Arrmanatha Nasir added he was "surprised" by the Australian foreign minister's statement and insisted Indonesia was doing its utmost to secure its borders.

"On the issue of border patrol and securing our waters, Indonesia is very committed even though our waters are about 3.25 million square kilometers (1.25 million square miles) and we have over 17,000 islands," he told AFP.

"Controlling our waters and our borders remain the number one priority for Indonesia, as reflected in our foreign policy."

Abbott's hardline immigration policy also involves sending asylum-seekers who arrive by boat to camps on the Pacific islands of Nauru and Papua New Guinea despite strong criticism from rights groups. They are banned from settling in Australia even if later found to be genuine refugees.

Only one boat with asylum-seekers has reached the Australian mainland since December 2013. Before the policy was introduced, boats were arriving almost daily, with hundreds drowning en route.

Abbott said at the weekend the key message for Indonesia was that his government was "prepared to do what's necessary" to prevent unwanted boats arriving in Australian waters.

Philip Ruddock, a senior lawmaker from Abbott's party and a former immigration minister, on Monday defended payments to turn boats back, without commenting on the specific allegations.

"The amount of money that was allegedly paid is nothing in comparison to the cost of processing the excessive amount of people who came to Australia as a result of people-smuggling activity," he was quoted by News Corp. as saying.

Labor immigration spokesman Richard Marles said the claims were affecting bilateral ties which were already strained after the execution in April of the Australian drug smugglers.

Asked if he agreed with Bishop, Marles replied: "I don't think now is the time for the Australian government to be walking down that path."