Precise measures must be taken to prevent a future imbroglio, he said, as he welcomed the letter sent by Australian Prime Minister Tony Abbott.
Mr Yudhoyono said that in the letter the Australian prime minister had given his commitment that Australia would not take any action in the future that would harm or upset Indonesia.
Stating that he is positive about the future of the bilateral relationship, Mr Yudhoyono said the two countries would work together to draft a new code of ethics for intelligence sharing.
The statements follow an almost month-long diplomatic spat over revelations that Australia’s Defence Signals Directorate tried to wiretap the phones of the Indonesian President, First Lady and other key ministers in 2009.
The spying revelations have irked Indonesians, who feel a sense of betrayal by their purportedly close neighbor.
In the wake of consecutive days of impassioned protests in front of the Australian embassy in Jakarta, Mr Yudhoyono called for calm, urging the country to refrain from overly emotional reactions.
But last week an angry Mr Yudhoyono responded quickly and harshly to the spying revelations, recalling the Indonesian ambassador to Australia and freezing all military cooperation.
The bilateral cooperation includes key joint patrols to curb the number of asylum seekers arriving on Australia shores, a cornerstone of Abbott’s election win.
Earlier today the Trade Minister Gita Wirjawan confirmed the spying row had taken its toll on business, admitting he had asked the parliament to consider importing beef from countries other than Australia.
"I think you can attribute some of that or a lot of it to the unfortunate incident that took place," he said.
With a market share of $174 million, Australian imports of live cattle currently dominate the Indonesian market.
Speaking after a meeting with several key advisors and ministers, the Indonesian president also called on his foreign minister to seek answers from other parties reportedly involved in the US-led spy network.
Neighboring Singapore, for example, in tandem with America’s National Security Agency, has reportedly been monitoring intelligence through tapping undersea cables.
On Tuesday Malaysia summoned the High Commissioner of Singapore for talks following the reports of the Singapore’s involvement.
Details of the wiretapping were revealed by the Australian media last week and follow previous revelations detailed in documents leaked by former National Security contractor, Edward Snowden.
The data showed that Australia sucesssfully wiretapped President Yudhoyono’s phone at least once in 2009, during the term of Labor prime minister Kevin Rudd.
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