Mr Abbott's office confirmed he no longer intended to travel to Bali on Tuesday for a meeting with Indonesian president Susilo Bambang Yudhoyono but declined to go into the reasons for putting off the visit, which had been seen as a thawing of ties tested by recent rows over espionage and Australia's controversial refugee policies.
"The prime minister was hoping to attend the Open Government Partnership conference in Bali next week at the invitation of His Excellency President Yudhoyono. The prime minister is grateful for the invitation," a spokesman for Mr Abbott told AFP.
"Unfortunately the prime minister is unable to attend at this time and he hopes to visit Indonesia to meet with the president at a mutually convenient time."
It would have been Abbott's first trip to Indonesia since damaging revelations in November that Australian spies attempted in 2009 to tap the phones of Yudhoyono, his wife and other members of his inner circle.
Jakarta reacted furiously to the news, recalling its ambassador and halting cooperation in key areas including defence and people-smuggling. Tensions were further inflamed by Canberra's military-led crackdown on asylum-seekers making their way to Australia by boat from Indonesia.
According to the Australian Broadcasting Corporation (ABC) next week's fence-mending trip was cancelled due to a people-smuggling vessel being intercepted in the sea corridor between the two countries under the "Operation Sovereign Borders" policy, where boats are turned back to Indonesia when it is safe to do so.
Citing government sources, the ABC said there were fears the mission would be an "embarrassment" to Yudhoyono if Abbott's visit went ahead.
The Australian government refuses to confirm or disclose details of its refugee turnback operations for security reasons.
The opposition Greens and Labor parties urged Mr Abbott to reveal his reasons for cancelling the trip, accusing him of further damaging ties with Jakarta by doing so.
"It's ironic that the invitation to Indonesia was to a conference on open government and our prime minister won't tell us why he's rejected the invitation at this late stage," said Labor foreign affairs spokeswoman Tanya Plibersek.
"It's very important the prime minister discloses the reason that he's not going, because Australians deserve to know why he's putting further pressure on the relationship with such an important neighbour."