Labor has abandoned its interrogation of the Abbott government over whether cash payments were made to members of Indonesian people-smuggling rings by Australian officials, after it was revealed that payments were also made under the former Labor government.

Fairfax Media reported that for at least the past four years payments to Australian intelligence officers have been made as part of successive governments' tactics, though not always as part of boat turnbacks, which were not used by the previous government.

On Monday, Labor hammered the government over the issue, even trying to force a censure against the government in Parliament. But it asked no questions in Tuesday's parliamentary question time, despite Mr Shorten vowing to Labor MPs in a caucus meeting that the Opposition would continue to pursue the matter.

Mr Shorten said no payments had been made to people smugglers to turn back boats. But he refused to comment on whether payments had been made for other reasons such as for intelligence or to dissuade boat crews from setting sail, citing intelligence and security reasons – the same reason as given by the government.

He told reporters: "I am informed that Labor did not pay people smugglers to turn around boats."

The issue of payments exploded into the public sphere with the claim last week, reported by Fairfax Media, that Australian officials paid $US5000 each to six crew members of an asylum-seeker boat crew to return the vessel to Indonesia.

Meanwhile, Foreign Minister Julie Bishop renewed her pressure on Jakarta, telling Fairfax Media that it was "vital for there to be an investigation into allegations that Indonesian police, military and officials are being bribed by people smugglers".

She said Australian officials continued to work "cooperatively and discreetly with their Indonesian counterparts".

Indonesia has demanded answers from the Abbott government about the payment allegations, with Indonesia's vice-president saying such "bribes" would be wrong and "definitely incorrect in the context of bilateral relations".

Fairfax Media has been told that the practice of intelligence agency officials paying members of people smuggling networks, including boat owners and crews, goes back to about 2010 under the then Rudd government. It is understood  at least one former Labor immigration minister knew of payments under his watch.

Instances include paying members of syndicates for information about the operations of the syndicate, or to dissuade them from launching boats.

The claim has sparked further tension between Canberra and Jakarta, with the Indonesian government demanding answers.

Ms Bishop, Mr Abbott and Mr Dutton have remained steadfast in their refusal to answer questions, citing intelligence, security and operational reasons.

Pressed again on the issue on Tuesday morning, Mr Abbott said Australia "will do whatever is necessary, within the law, consistent with our standards as a decent and humane society to stop the boats".

"I am absolutely confident that at all times Australian agencies have acted within the law," Mr Abbott said. "I am in the business of supporting our agencies, not undermining them."