Prime Minister Tony Abbott and Indonesian President Susilo Bambang Yudhoyono have had constructive discussions about fighting the "scourge" of people smuggling together.
Speaking after their meeting in Jakarta on Monday, Mr Abbott said they had frank talks and stressed his respect for the sovereignty of Australia's northern neighbour.
"We have had very cordial, constructive and collegial discussions on the issue of people smuggling," he said.
"We are resolved together united to tackle this problem and to beat it - on land and at sea, and at the borders of our countries," Mr Abbott said.
"We are determined to end this scourge which is not just an affront to our two countries, but which has so often become a humanitarian disaster in our seas between our two countries."
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The meeting between the two leaders came just days after the tragic sinking of an asylum seeker boat off the coast of Indonesia, and with tensions between the two countries about how to tackle the problem.
Indonesia has raised concerns about the coalition's `turn back the boats' policy, which Indonesian foreign minister Marty Natalegawa last week warned could violate his country's sovereignty and damage relations.
Mr Abbott said he and President Yudhoyono had held "very frank" discussions about "issues of sovereignty and about issues of people smuggling".
"People smuggling is an issue of sovereignty, especially for Australia," Mr Abbott said.
"I appreciate how seriously Indonesia has taken this issue in the past, and I look forward to working even more co-operatively with Indonesia on this issue in the future.
"But I do want to stress publicly as well as privately ... Australia's total respect for Indonesia's sovereignty, total respect for Indonesia's territorial integrity."
Mr Abbott said he acknowledged there had been mistakes in the past and he wanted a new start to the relationship, particularly in agriculture and food security.
"Never again should this country take action that jeopardises the food supply of such a friend and partner as Indonesia is," he said.
Mr Abbott also said he admired what Indonesia had done to improve the autonomy and life of people in West Papua.
"I am confident that they can have the best possible life and the best possible future as a part of an indissoluble Indonesia, as an integral part of Indonesia."
