Updated

The political row over spying allegations that has ratcheted up tensions between Indonesia and Australia appeared to have softened after Australian Prime Minster Tony Abbott responded to concerns from his Indonesian counterpart.

Indonesia President Susilo Bambang Yudhoyono told reporters he will send Foreign Minister Marty Natalegawa or a special envoy to Australia to discuss creating a code of conduct that would allow the two countries to continue cooperating on a number of issues, including intelligence information sharing, military and police.

Yudhoyono sent a letter to Abbott outlining his concerns and received a quick reply.

"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.

Last week, Natalegawa said Jakarta was downgrading its relations with Australia. Cooperation between the countries' law enforcement agencies and militaries was suspended, including work on the thorny issue of people smuggling. Indonesia also recalled its ambassador to Australia.

Abbott has refused to confirm or deny that the president, his wife and other leaders' phones were bugged in 2009, and he will not apologize over the allegations reported on from documents provided by National Security Agency leaker Edward Snowden.

Yudhoyono also responded to new published allegations in the Sydney Morning Herald from 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 with 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.