INDONESIA has dramatically halted military ties with Australia and stopped co-operation in the fight against people smugglers in an angry backlash over spying claims.

Tony Abbott was facing his first real crisis as Prime Minister after Indonesian President Susilo Bambang Yudhoyono stepped up the diplomatic row.

He also froze information-sharing on counter-terrorism, in a televised speech demanding an apology.

Dr Yudhoyono's retaliation threatens to scuttle Mr Abbott's key election promise to "stop the boats", because he needs Indonesia's help.

In recent weeks Indonesia has arrested suspected people smugglers and stopped boats carrying 1200 asylum seekers travelling to Australia.

Dr Yudhoyono said the people of Indonesia were "very annoyed and they're very angry" over allegations Australia tried to tap his mobile phone, as well as those of his wife and eight other top figures, in 2009 when Kevin Rudd was prime minister.

Mr Abbott has refused to apologise, but has called on Jakarta not to "overreact", telling the House of Representatives on Wednesday night he offered "my deep and sincere regret about the embarrassment to the President and to Indonesia that's been caused by recent media reporting".

Mr Abbott has not confirmed spying by Australia's top secret Defence Signals ­Directorate took place after information was leaked by US whistleblower Edward Snowden, who fled to Russia.

Indonesia says Australian intelligence officials said there would be "no more tapping".

Dr Yudhoyono said he wanted an apology from Mr Abbott and a new legally binding "code of conduct" for all ­future co-operation.

"It is not possible we can continue our co-operation when we are still uncertain that there is no spying towards us," Dr Yudhoyono said.

He said there would be a "halt" of co-operation, exchange of intelligence and joint military training for the army, navy and air force.

Australian and Indonesian special forces and air force were conducting joint anti-terror war games in the Northern Territory.

Dr Yudhoyono will be standing down next year.

He shocked the Government by launching a series of attacks on Twitter on Tuesday and then on Wednesday giving a televised speech in Indonesia announcing the relationship had been "downgraded".

Mr Abbott delayed a speech to business leaders in Canberra on Wednesday to tell Parliament he would respond to Dr Yudhoyono "swiftly, fully and ­courteously".

"I have to say that I was encouraged by the President's remarks about the strength of the relationship between Australia and Indonesia although obviously there are very serious issues which do need to be worked through in the near future between us," he told Parliament. Mr Abbott earlier said he would not "overreact" .

"I do note that there have been allegations and even admissions in the past on this subject," he told Parliament.

"People didn't overreact them and I certainly don't propose to overreact now."

Opposition Leader Bill Shorten said Labor was behind the Government in repairing the relationship quickly.

"We do not underestimate the seriousness of this matter or the sense of offence that our Indonesian friends have felt."

Indonesian Foreign Minister Marty Natalagawa said it was Australia's actions in spying that were embarrassing.

"The embarrassment should belong to the Government of Australia, to Australia, not to Indonesia," he said.

Originally published as Spy farce as Abbott refuses to give in