Indonesia has twice knocked back requests from the Abbott government to take asylum seekers picked up by the Australian Navy in their waters.
Immigration Minister Scott Morrison made the comments after responding to a Jakarta Post report on Saturday, in which an Indonesian MP said they had declined three out of six Australian requests since September.
Mr Morrison, however, says Australia made four requests for transfer, of which two were rejected.
"I have given the Indonesian government an assurance that we would not canvass these requests publicly when and if they are made and I intend to honour that commitment," Mr Morrison said.
"For the sake of correcting the public record, our post had made four such requests under Operation Sovereign Borders. Two were accepted and two were not."
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Prime Minister Tony Abbott says the coalition's plan to stop the boats is working despite there being setbacks.
Critics, however, say Jakarta's refusals signal a crack in the government's border protection policy.
Labor criticised the coalition's policy of turning back the boats, saying it simply wasn't working.
"The border protection policy which Tony Abbott took to the election is in tatters," opposition immigration spokesman Richard Marles said.
The Australian Greens have called on the government to end its secrecy over border security operations, outlining plans to move a motion in parliament next week compelling the government to release details.
"Mr Abbott's excuses for secrecy are wearing thin and the Greens will use the powers of the Parliament to reinforce transparency," the minor party's immigration spokeswoman Sarah Hanson-Young said.
"The coalition's turnaround policy is in tatters and it is time that Mr Abbott admitted that he had it wrong from the start."
