Reports last month that Australian spies tried to tap the phones of Indonesian President Susilo Bambang Yudhoyono, his wife and several top officials in 2009 sparked one of the worst diplomatic crises between the two strategic allies in years.
"Obviously we regret the events that led to this situation. We regret the hurt caused to President Yudhoyono and to the Indonesian people," Australian Foreign Minister Julie Bishop said after a meeting with her Indonesian counterpart.
Jakarta had responded furiously to the espionage reports, based on documents leaked by US intelligence fugitive Edward Snowden, suspending bilateral cooperations with Australia in key areas including over people-smuggling.
Bishop said she and Indonesian Foreign Minister Marty Natalegawa had agreed to establish more open lines of communication, "a hotline, if you like", as a first step towards resuming cooperation and "avoiding any unintended consequences".
She also said Canberra had agreed to a six-point plan laid out by Yudhoyono last week, aimed at establishing a code of conduct to restore trust.
"We note the steps set out by President Yudhoyono that must be taken in order to normalise the relationship and of course we agree to adhere to those steps," Bishop said.
Canberra will not undertake "any act or use our asset or resources, including our intelligence assets, in any way to harm Indonesia", she added.
Natalegawa said the suspension in cooperation would remain in place until the code of conduct was finalised, but said that the meeting with Bishop was "constructive" and that Yudhoyono was "pleased by the progress made today".
"I did not share any specific deadline (with Australia), except I remind (them) once again we have the six steps to go through. We are now at step one," he said.
Bishop will also visit China, where relations are likewise on edge after Canberra's criticism of Beijing's new air defence identification zone, which covers East China Sea islands disputed with Japan.