Australia’s new Prime Minister Tony Abbott has made his first official visit since assuming duty last week to Indonesia.

Speaking at a meeting with the Indonesia President Susilo Bambang Yudhoyono, Mr Abbott said Australia respected Indonesia’s sovereignty and territorial integrity. The meeting between the two countries was to discuss on asylum seekers.

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.