Prime Minister Tony Abbott's claim that Australian intelligence gathering is done chiefly to save lives is being tested, with reports of spying on Indonesian-US trade talks over shrimp.
Whistleblower Edward Snowden's latest leak, to The New York Times, came as US Secretary of State John Kerry visited Jakarta.
The report claims Australia's Defence Signals Directorate offered its US counterpart information on trade talks with Indonesia last year.
Mr Abbott will not confirm the report, or address whether the latest leaks have further damaged ties with Indonesia.
"If the media wants to talk constantly about this kind of thing inevitably it will dominate conversation," he told ABC radio.
At a media conference alongside Mr Kerry on Monday, Indonesia's Foreign Minister Marty Natalegawa said it was "a little bit too much" to argue this latest activity was done in the interest of saving lives.
"I find that a bit mind-boggling and a bit difficult - how I can connect or reconcile discussion about shrimps and how it impacts on Australia's security," he said.
Mr Kerry said he understood why Indonesia had concerns over the spy reports, an issue that was "a challenge for all of us".
Revelations last year that Australia spied on Indonesian President Susilo Bambang Yudhoyono and members of his inner circle - coupled with Australian incursions into Indonesian waters as part of its asylum boat turnback policy - have sent bilateral relations plummeting.
Mr Abbott has defended spying on its "very good friend" Indonesia, arguing intelligence is gathered in the interest of Australian citizens.
Indonesia, meanwhile, has suspended all military, police and intelligence co-operation pending agreement on a code of conduct.
The Reuters news agency reports it has seen a document from a January meeting of Indonesia's Coordinating Ministry for Political, Legal and Security Affairs, which says Jakarta does not expect diplomatic links to be restored until October.
Mr Abbott on Monday agreed progress had been slow, telling ABC radio: "I'd like it to progress much faster".
Dr Natalegawa was also expected to use the talks with the US to raise his concerns about Australia's policy of turning back asylum-seeker boats.
The minister has repeatedly expressed discomfort with the policy, questioning whether the Australian government is meeting its obligations under the UN refugee convention.
Jakarta-based international relations expert Hikmahanto Juwana says his raising of the issue with Mr Kerry ups the stakes, making the policy an international issue - not just a bilateral issue.
"Indonesia in this context seems to be gathering a coalition with other countries to condemn Australia, which is not paying attention to human rights with its policy of pushing back asylum seekers," he said.
If Mr Abbott wants to speed up the process of reconciliation, he needs to make a more comprehensive and personal apology, the University of Indonesia expert said.
"The Australian government must also make a clear statement stating that they will not repeat it in the future," Prof Juwana said.