Indonesia's president says ties with Australia have been "damaged" by reports that Canberra spied on his phone calls and those of his ministers.
Susilo Bambang Yudhoyono said it was a "hurtful action" and that Australia had "belittled" the row. Jakarta would review co-operation, he said.
Australian PM Tony Abbott expressed regret but said he would not apologise.
The allegations published by Australian media came from documents leaked by whistleblower Edward Snowden.
Mr 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.
However, he added: "I don't believe that Australia should be expected to apologise for reasonable intelligence-gathering operations, just as I don't expect other countries or other governments to apologise for their reasonable intelligence-gathering operations."
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.
The presentation from the Defence Signals Directorate (now known as the Australian Signals Directorate) showed that agencies attempted to listen to Mr Yudhoyono's calls at least once, and tracked calls made to and from his mobile phone, in August 2009, they added.
It is the latest in a series of spying allegations that have strained relations between the two allies.
Earlier this month, Indonesia expressed anger over reports that Australia's Jakarta embassy was used as part of a US-led spying network in Asia.
On Tuesday, in a series of strong tweets, Mr Yudhoyono said: "These US & Australian actions have certainly damaged the strategic partnerships with Indonesia, as fellow democracies."
He said that Indonesia would review its "bilateral co-operation agenda" with Australia.
He also expressed "regret" at Mr Abbott's response to the allegations, saying that he had "belittled this tapping matter on Indonesia, without any remorse".
Speaking in parliament on Monday, Mr Abbott had said: "The Australian government never comments on specific intelligence matters."
"All governments gather information and all governments know that every other government gathers information," he said.
"I will never say or do anything that might damage the strong relationship and the close co-operation that we have with Indonesia, which is all in all our most important relationship."
The alleged spying took place in 2009, under the previous government.
Australia and Indonesia are key allies and trading partners.
Australia requires Indonesia's co-operation on asylum, as many asylum seekers travel via Indonesia to Australia by boat, but there are tensions on the issue.
Earlier this month, Indonesia declined an Australian request to receive a boat of asylum seekers whose vessel, bound for Australia's Christmas Island, had got into trouble after it departed from Indonesia.
Monday's leaked document, a slideshow presentation, appeared to show a list of Indonesian "leadership targets" and the handset models used by each target, as well as a diagram of "voice events" of the Indonesian president in August 2009.
One slide entitled "Indonesian President voice intercept (August '09)" appeared to show an attempt to listen to the content of a phone call to Mr Yudhoyono.
It is amongst a series of documents leaked by ex-US intelligence contractor Edward Snowden, who has been granted temporary asylum in Russia and is wanted in the US in connection with the unauthorised disclosures.