The Indonesian president, Susilo Bambang Yudhoyono, has accused Tony Abbott of “belittling” Australia’s attempts to tap his phone and those of other senior Indonesian politicians.

Tweeting in Bahasa on his official account, Yudhoyono said: “I regret the Australian PM statement belittling the phone-tapping in Indonesia without feeling guilty. We are reviewing a number of co-operation agendas because of the damaging Australian behaviour … The action by the US and Australia is damaging the strategic partnership with Indonesia, a democratic nation.”

The Australian prime minister has refused to apologise for, or even talk about, the revelations of attempted spying against Indonesia revealed on Monday by Guardian Australia and the Australian Broadcasting Corporation, saying to do so was not in the interests of the bilateral relationship.

On Tuesday Abbott continued to insist it was in the best interests of the bilateral relationship for him not to comment, though he acknowledged this was “obviously not the best day” in Australian-Indonesian relations.

“I’m not going to say anything about intelligence matters. It’s never been the custom or the practice of Australian governments to comment on these things and I don’t propose to change that practice now,” Abbott said as he was leaving an event in Canberra.

“The truth is that we have a very good relationship with Indonesia. Obviously today might not be the best day in that relationship … but ... it’s in no one’s interests to do anything or say anything that would jeopardise that relationship and certainly I’m not going to.”

Bob Carr, Labor’s foreign minister from 2012, has said the government must apologise for the spying and “carve out what is off limits” for intelligence gathering in future.

Carr said the revelations were “nothing short of catastrophic” for the bilateral relationship and that Abbott’s response to date had been “too dismissive by far”.

Carr suggested Abbott could apologise and then agree to “carve out areas we won’t touch” in a similar way to Barack Obama’s statement that the US was not currently monitoring the phone of the German chancellor, Angela Merkel, and would not do so in future.

Carr also suggested ministers would have “signed off” on the decision to spy on the Indonesian president, his wife and his inner circle, saying “you’d like to think the hand of a minister would hover before signing off” on such a proposal.

He said ministers should have considered whether the gains from such eavesdropping were “so vital” that they outweighed the risk to national security of the practice becoming publicly known.

Guardian Australia understands from several intelligence sources that the defence minister would normally have to approve such high-level surveillance targets. That minister was Joel Fitzgibbon until June 2009, and then John Faulkner. Both have declined to comment.

The revelations come from a Defence Signals Directorate (DSD) slide presentation dated November 2009, during the former Labor administration.

Indonesia recalled its ambassador toAustralia and is reviewing all co-operation. Indonesia’s foreign minister, Dr Marty Natalegawa, said he was "flabbergasted" by the revelations, which he described as “nothing less than an unfriendly act” which “violates every single decent and legal instrument I can think of”.

Indonesia's co-ordinating minister for politics, law and security, Djoko Suyanto, has demanded a public explanation from Abbott within two days.

Indonesia’s ambassador, Nadjib Riphat Kesoema, returned to Canberra from Brisbane on Tuesday morning and was due to fly to Jakarta later in the day.

The Greens senator Scott Ludlam is writing to the inspector general of intelligence and security, Vivienne Thom, asking that she conduct an inquiry into Australian spying on foreign heads of state.

The documents, published by the Guardian and the ABC and leaked by the NSA whistleblower Edward Snowden, show that the DSD targeted the phones of Yudhoyono and his wife, as well as those of eight other high-profile Indonesian politicians, among them possible successors to Yudhoyono.

Addressing the leak on Monday, Abbott said "all governments gather information and all governments know that every other government gathers information" and vowed that Australia used "resources at [their] disposal, including information, to help our friends and our allies, not to harm them".

Natalegawa dismissed these claims. "I have news for you," he said. “We don't do it. We certainly should not be doing it among friends.” He said he was unhappy with the "dismissive answers being provided" by Canberra.

The leak is a slide presentation, marked top secret, dealing with the interception of mobile phones as 3G technology was introduced in Asia. It includes one slide titled “Indonesian President Voice Intercept”, dated August 2009, and anothe, titled “IA Leadership Targets + Handsets”, listing the president and the first lady as having Nokia E90-1s, Boediono as having a BlackBerry Bold 9000, and the type and make of the mobile phones held by the other targets.

Also named as targets for the surveillance are Dino Patti Djalal, at the time the president's foreign affairs spokesman, who recently resigned as Indonesia's ambassador to the US and is seeking the candidacy in next year's presidential election for the president's embattled Democratic party, and Hatta Rajasa, now minister for economic affairs and a possible presidential candidate for the National Mandate party. Hatta was at the time minister for transport and his daughter is married to the president's youngest son.