But Yudhoyono said he has received a quick reply to a letter he sent to Abbott outlining his concerns.
"The Australian prime minister's commitment is that Australia will not do anything in the future that will be detrimental or disturb Indonesia," Yudhoyono said, without providing specifics. "This is the important point."
Abbott welcomed Yudhoyono's statement and described the proposed code of conduct as a "good way forward."
"It was a very warm statement. It was a statement that was very positive about Australia," Abbott told reporters in Melbourne on Wednesday.
"I'm going to reflect on the statement over the next day or so and then we'll be responding more fully," he added.
Yudhoyono also responded to new published allegations in the Sydney Morning Herald from the leaked documents that Singapore and South Korea helped the United States and Australia tap phones in Asia. He has instructed Natalegawa to summon both countries' ambassadors for questioning about the issue.
South Korea Foreign Ministry spokesman Cho Tai-young told reporters Wednesday that his government was not involved in spying and that its ambassador had explained that to the Indonesians during the meeting.
"I would like to make it clear that the report is false," Cho said.