Indonesian President Susilo Bambang Yudhoyono is said to be disappointed that a letter sent to him by Prime Minister Tony Abbott did not contain an apology for the spying that targeted him and his inner circle.

Dr Yudhoyono has demanded Australia sign a code of conduct that will address the spying issue, insisting that an agreement must be ratified before relations between Jakarta and Canberra can return to normal.

While Dr Yudhoyono on Tuesday night welcomed a commitment in the letter from Mr Abbott that "Australia would not do anything in the future" that would cause harm or damage to Indonesia, a senior Indonesian minister has said the president remains angry that there was no apology.

Industrial Minister Mohamad Suleman Hidayat was quoted in the Koran Tempo newspaper on Wednesday as saying that Dr Yudhoyono was disappointed the letter from Mr Abbott only contained a statement of regret for eavesdropping activities that targeted the president, as well as his wife and inner-circle, in 2009.

"The president is not embarrassed, he's angry. Tell Australia, I'm angry," Mr Hidayat said, according to Koran Tempo.

President Yudhoyono and Mr Abbott have agreed to appoint special envoys to discuss the proposed code of conduct, with the Indonesian leader expected to insist it includes "protocols" and guarantees that the phones of Indonesian politicians will not be monitored in the future.

The resumption in bilateral ties, as well as military and police co-operation, would be conditional on agreement on the new "code of ethics and protocols" which will map out the future relationship, Dr Yudhoyono said.

Foreign Minister Marty Natalegawa or another senior envoy will be assigned to handle negotiations.

Mr Abbott said he would take some time before fully responding to Dr Yudhoyono's statement, but embraced the idea of an envoy meeting.

"I think that's a good way forward," he told reporters in Melbourne.

"I'm going to reflect on the statement over the next day or so and then we'll be responding more fully."

The prime minister said he would like to see a security round table established in the future, so both nations could be more open with each other and build greater mutual trust.

"Obviously, that relationship does depend on a great deal of intelligence sharing," he said.

"I want to deepen and extend that in the weeks and months ahead."

Mr Abbott would not comment on what pledges he made in his letter to Dr Yudhoyono about phone tapping.

The developments come as Malaysia's foreign ministry summoned a senior Singaporean diplomat over allegations the city-state helped the US and Australia tap telecommunications links in Asia.

Singapore's government has not publicly responded to the allegations, which were published on Monday.

Dr Yudhoyono has asked the Indonesian Foreign Ministry to also seek answers over the latest allegations in case Indonesia was targeted.