General Sutarman said on Tuesday that he will order that cooperation be ceased immediately if directed to do so by President Susilo Bambang Yudhoyono.
"We have cooperation with Australia, but if the president orders us to stop, then we will do so," General Sutarman, who has been in the top job for less than a month, was quoted as saying in local media.
"The Indonesian National Police and AFP (Australian Federal Police) cooperate in training and cyber crime, laboratory support. This is in the form of police-to-police cooperation.
"We're ready to stop."
Indonesian police and the AFP have cooperated widely since the Bali bombings and a suspension in joint operations could have serious implications for efforts aimed at stopping asylum-seeker boat traffic.
The comments from General Sutarman come in the wake of claims Australia spies had monitored the phone activity of Dr Yudhoyono in 2009.
Indonesia's Coordinating Minister for Legal, Political and Security Affairs Djoko Suyanto on Monday demanded Australia make a public explanation about the claims.
Marshal Suyanto also said Indonesia would review the exchange of information with Australia and "all other cooperation".
It's alleged Australia's Defence Signals Directorate also monitored the phone activity of the president's wife Kristiani Herawati, better known as Ibu Ani, as well as that of Vice President Boediono and former vice president Jusuf Kalla.
It has been alleged the president's mobile activity was tracked for 15 days during August 2009 and at least one eavesdropping attempt was made.
AUSTRALIA CAN'T BE EXPECTED TO APOLOGISE: PM ABBOTT
Earlier today, Prime Minister Tony Abbott told his coalition colleagues he believes his team is responding intelligently to the demands of government, including the escalating tensions with Indonesia.
Mr Abbott addressed a joint coalition party room meeting in Canberra on Tuesday, telling MPs and senators that his government is "purposefully, calmly and methodically" getting on with the business it was elected to do.
He said the government had had a good two weeks and was "intelligently responding to the exigencies of the day", making a fleeting reference to the tensions between Australian and Indonesia over spying claims.
Colleagues praised Mr Abbott's recent visit to Sri Lanka for the Commonwealth Heads of Government Meeting.
Mr Abbott told the meeting he has "no interest in taking sides in fights in other countries", referring to his decision not to raise human rights concerns with the Sri Lankan government.
Mr Abbott said the Labor party was consumed with one question: was Kevin Rudd or Julia Gillard a worse prime minister?
He said he had settled on Mr Rudd because he did not even resign from parliament properly, subjecting the people of Griffith to three months without a member of parliament before a by-election can be held.
Deputy Prime Minister Warren Truss also spoke about regional infrastructure funding, saying he had no intention of delivering on all Labor's promises.
However the government would conduct a "proper merit analysis" of individual Labor projects and may proceed with some, he said.
WHAT HE SAID: The Indonesian President's tweets, translated
"Since information emerged concerning the US and Australia tapping phones in a number of countries, including Indonesia, we have made strong protests."
"The foreign minister and government officials are also taking effective diplomatic steps, while requesting explanations and clarifications from the US and Australia."
"Today I am instructing Foreign Minister Marty Natalegawa to recall to Jakarta Indonesia's ambassador to Australia."
"Indonesia is also requesting Australia to provide an official response to the phone-tappings in Indonesia that can be understood by the broader community."
"We will also review a number of bilateral cooperation programs as a result of Australia's hurtful behaviour."
"These actions by the US and Australia have been extremely harmful to their strategic partnership with Indonesia, a fellow democratic nation."
"I also deplore the statement by the Australian PM, who trivialised the phone-tapping directed against Indonesia and showed no remorse."
