On a trip to Jakarta, where officials have complained his plans to tackle asylum-seekers arriving by boat threaten Indonesian sovereignty, Abbott said he was encouraged by the response he received at a critical meeting with President Susilo Bambang Yudhoyono.
"I made it very clear that this is an issue of sovereignty for us and I think I can say that on the Indonesian side, there was a willingness to be as co-operative as was possible to ensure this evil scourge is ended," he told reporters.
Abbott won a landslide election in September with his "stop the boats" mantra, which involved plans to tow asylum-seeker vessels from Australian waters and buy boats from Indonesian fishermen to prevent people smugglers buying them first.
While his policies helped propel him to power in Australia, they caused consternation in Indonesia, with Foreign Minister Marty Natalegawa and lawmakers lining up to criticise them.
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But on his visit to Jakarta, his first overseas trip since becoming premier, Abbott has striven to strike a conciliatory tone as he seeks to strengthen business ties with Southeast Asia's biggest economy.
"Can I just scotch this idea that the coalition's policy is, or ever has been, 'tow-backs'," he said.
"Tow-back" is a term that has been widely used to refer to his plans for Australian navy boats to take boats back to Indonesia when it is safe to do so.
It has been the main reason why officials in Jakarta became concerned that his policies may breach Indonesian sovereignty.
"Our policy, which we've repeated till we're blue in the face, is that we reserve the right to turn boats around where it's safe to do so," he said.