Indonesian President Susilo Bambang said ties with Australia have been "damaged" by reports that Canberra spied on his phone calls and those of his ministers, the BBC reported on Tuesday.
Susilo Bambang Yudhoyono said the "hurtful action" had led Indonesia to review its co-operation with Australia.
Australian Prime Minister Tony Abbott had "belittled" the row, he added in a series of angry tweets.
The allegations came from documents leaked by whistleblower Edward Snowden which were published by broadcaster ABC and the Guardian newspaper.
Australian Prime Minister Tony Abbott said he regretted "any embarrassment" caused by the reports.
"I regard President Yudhoyono as a good friend of Australia, indeed as one of the very best friends that we have anywhere in the world," he said.
Indonesia recalled its ambassador on Monday, after the latest allegations emerged, and said it was summoning Australia's ambassador for questioning.
The leaked document showed that Australian spy agencies named Mr Yudhoyono, the first lady, the vice-president and other senior ministers as targets for telephone monitoring, the Australian Broadcasting Corporation (ABC) and the Guardian said.