Former prime minister Julia Gillard has suggested Tony Abbott follow the example of US President Barack Obama and provide Indonesia with an explanation of spying allegations.
But she stopped short of saying the prime minister apologise for the actions of Australia's electronic spy agency in 2009.
Ms Gillard said it was not appropriate for her to comment on intelligence matters but she praised the way Mr Obama handled similar allegations of US phone taps on German Chancellor Angela Merkel.
"If he had been aware he wouldn't have authorised it, and he could certainly say for the future that it wouldn't happen again," she told CNN.
"I think that that's an appropriate response from Australia to Indonesia at this very difficult time."
Labor MP Matt Thistlethwaite repeated Opposition Leader Bill Shorten's suggestion earlier in the week that Mr Abbott consider the same approach.
"Barack Obama appears to have been able to calm the situation and normalise relations by taking action," he told Sky News.
Former foreign minister Alexander Downer believes Mr Obama went too far in confirming the US had been listening to Ms Merkel's phone and promising that it would never happen again.
"If Tony Abbott were to say `gee I'm sorry about that', that would reveal that in fact, the allegation was true," he told Sky News.
Mr Downer said it had been the doctrine of Australian governments for generations neither to confirm nor deny claims relating to the nation's intelligence services.
If the doctrine was abandoned then every time an allegation was made you would have to say whether it was true or whether it was false.
"As you do that, the whole intelligence system ... will gradually unravel."
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