Australia's new conservative government, led by Prime Minister Tony Abbott who swept to power in national polls earlier this month, hopes to deter asylum-seekers from taking people-smuggling boats with the threat of potential towbacks.
Indonesia's top diplomat Marty Natalegawa had warned Bishop during their meeting in New York on Monday that Jakarta could not accept any policy which infringed its sovereignty, Antara news agency reported.
Bishop said she had spoken to Natalegawa about Australia's military-led operation to shut down people-smuggling networks, which includes forcing their boats to turn around when conditions are safe.
"I am not going into the operational details of our policy, but I had a very broad-ranging discussion with... Natalegawa and I am confident that we will be able to implement our policies."
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Natalegawa told reporters that "Indonesia cannot accept any Australian policy that would, in nature, violate (our) sovereignty".
"I think, the message has been conveyed loud and clear and has been understood well."
Asked whether Natalegawa had indicated that he was unhappy with Australia's plan, Bishop said: "There can be some misunderstanding as to what our policy is, and it is certainly not to, in any way, show disrespect for Indonesian sovereignty."
She blamed the previous Labor government of leaving "a complete mess in border protection" which she said encouraged people-smuggling, although boat arrivals slowed sharply ahead of the elections due to their tough permanent resettlement deal for refugees with Papua New Guinea and Nauru.
Bishop said that she looked forward to further talks during Abbott's upcoming visit to Indonesia, where he will meet President Susilo Bambang Yudhoyono on September 30.