Labor says Australia must sign a code of conduct with Indonesia before the relationship could be considered back on track.
Prime Minister Tony Abbott held talks with President Susilo Bambang Yudhoyono in Indonesia on Wednesday in a bid to repair ties damaged by last year's spying scandal.
Following the meeting, both leaders expressed a wish to finalise a code of conduct on intelligence gathering soon - and to move on from the revelations that Australian spies had targeted the phones of Dr Yudhoyono's inner circle.
Dr Yudhoyono, who leaves office later this year, wants it done by August.
Mr Abbott says it will likely happen when foreign ministers Julie Bishop and Marty Natalegawa meet in the coming weeks.
Labor frontbencher Tony Burke welcomed the talks between the leaders, but said the opposition had hoped the code of conduct would be signed on Wednesday's visit.
The code was "the signal we need to see", he said.
"That will really set a mark in terms of some of the issue that came up at the end of last year," Mr Burke told Sky News on Thursday.
"You want it done and sorted as quick as possible.
"The code of conduct was a signal that Indonesia gave as something that was important to be able to get things back on track."
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