The Australian Signals Directorate logged the president's calls for a 15-day period in 2009, national broadcaster ABC reported, citing former US security worker Edward Snowden.
The service also tried unsuccessfully to listen in to one of the calls, the report said.
Australian Prime Minister Tony Abbott defended the country's intelligence practices. "All governments gather information," he told parliament Monday, saying he was "aware of media reports" on the latest revelation of Canberra's alleged spying on its South-East Asian neighbour.
"My first duty is to protect Australia and to advance our national interest," Abbott said.
"I'll never ever depart from that. Consistent with that duty I'll never say or do anything that might damage the strong relationship and the close cooperation that we have with Indonesia." The claims relate to a time when Labor was in government rather than Abbott's Conservatives.//DPA