Australian Prime Minister Tony Abbott on Tuesday offered no apology and insisted relations with Indonesia remained close and strong despite spying allegations that sparked a furious reaction from Jakarta.

Indonesia on Monday recalled its ambassador from Canberra in response to reports that Australian intelligence agencies tapped the phone calls of President Susilo Bambang Yudhoyono as well as his wife and senior ministers.

Jakarta said it was "flabbergasted" by the revelations in documents leaked by US intelligence fugitive Edward Snowden to the Australian Broadcasting Corporation and The Guardian newspaper, and vowed to review all cooperation with Australia.

Abbott refused to say if he planned to contact Yudhoyono directly to offer an explanation or an apology.

"I'm just not going to say anything or do anything that could possibly damage our close friendship and strong cooperation with Indonesia, I'm just not going to say anything about intelligence matters," he told reporters.

"The truth is we have a very good relationship with Indonesia.

"Obviously, today may not be the best day in that relationship. But nevertheless, we do have a very good and strong relationship with Indonesia."

Abbott added: "It's in no one's interest to do anything or say anything that would jeopardise that relationship and certainly I'm not going to."

The documents show that Australia's electronic intelligence agency tracked Yudhoyono's activity on his mobile phone for 15 days in August 2009, when Labor's Kevin Rudd was prime minister.

Weeks before, twin blasts at luxury hotels in the Indonesian capital -- the JW Marriott and Ritz-Carlton -- had killed seven people, including three Australians, as well as two suicide bombers.

The directorate reportedly intercepted at least one call.

The list of 10 tracking targets also included Yudhoyono's wife Ani, Vice President Boediono -- who was in Australia last week, former vice president Jusuf Kalla, the foreign affairs spokesman, the security minister and the information minister, the reports said.

On Monday, Indonesian Foreign Minister Marty Natalegawa called the spying claims "an unfriendly, unbecoming act between strategic partners".

"This isn't a smart thing to do," he said. "It violates every single legal instrument that I can think of in Indonesia and Australia and on an international level as well."

The row heaped fresh pressure on ties between the two neighbours and strategic allies, which were already strained due to Abbott's tough policy of turning back asylum boats heading for Australia to Indonesia.

They also took a hit when earlier Snowden documents claimed Canberra's overseas diplomatic posts, including in Jakarta, were involved in a vast US-led surveillance network, prompting Indonesia to summon the Australian ambassador.

Former US National Security Agency contractor Snowden was given asylum in Russia in August, to the fury of the United States where he is wanted on espionage charges following disclosures that have provoked international uproar.