Australia's new Prime Minister Tony Abbott, who is in Indonesia on his first official foreign visit, has said the two countries are "united" on the issue of asylum seekers.
After talks in Jakarta with President Susilo Bambang Yudhoyono, Mr Abbott said Australia respected Indonesia's sovereignty and territorial integrity.
Mr Yudhoyono said the solution was co-operation between the two nations.
At least 31 asylum seekers drowned off the Java coast last week.
Speaking to reporters after Monday's talks, Mr Abbott said the two leaders agreed on how to tackle the problem.
"We are determined to end this scourge," he said, "which is not just an affront to our two countries, but which has so often become a humanitarian disaster in the seas between our two countries."
Jakarta has previously expressed concern over Mr Abbott's policy of sending boats with illegal migrants back to Indonesia - and warned that the move could breach the country's sovereignty.
But Mr Abbott reassured his hosts that Australia had total respect for Indonesia's sovereignty and territorial integrity.
'Stand or fall'
The Liberal party leader, whose "stop-the-boats" policy helped propel him to power in September's elections, said that stopping the flow of asylum seekers to Australia was a "stand-or-fall" issue for him.
Many migrants, especially from Afghanistan and the Middle East, use Indonesia as a stopping point as they try to reach Australian shores and claim asylum.
Many head for the remote Indian Ocean territory of Christmas Island, and hundreds of people have died en route there in recent years.
Ahead of the tour, Mr Abbott sought to play down the tensions over asylum issues, saying he planned to focus on other subjects, including trade.
He brought a delegation of 20 Australian business leaders to Jakarta, and said a new Australian-Indonesia study centre would be created.
Mr Abbott has said in the past that he wants "more Jakarta and less Geneva" in Australia's foreign policy, and he stressed the symbolic importance of this trip.
"It is my hope that this visit establishes a convention for all future incoming prime ministers to make Jakarta their first port of call overseas," Mr Abbott said.
But according to the BBC's Karishma Vaswani in Jakarta, this trip was more about appeasing Indonesia on the asylum issue rather than achieving anything concrete.
The visit comes just three days after a boat packed with asylum seekers sank off the coast of Java island, killing at least 31 people.
It is not clear how many were on the boat, but some reports say between 80 and 100 people were on board.
Survivors have since accused the Australian navy of failing to respond.
Canberra says it provided all appropriate assistance to the vessel.