He also stressed the importance of boosting economic ties between the countries from the current 14.6 billion Australian dollars ($13.6 billion) a year. He said a new Australian-Indonesia study center would be created at Monash University in Melbourne and that more Australians will be encouraged to pursue higher education in Indonesia.
"The new government's approach is very, very straightforward. We will take a respectful, consultative, no-surprises approach to relations with Indonesia," Abbott said Tuesday at the morning meeting attended by Indonesia's trade and finance ministers. "Our aim is to rebuild confidence so that both sides can respect each other and trust each other to keep commitments."
Abbott was accompanied on the two-day trip by Foreign Minister Julie Bishop, Trade Minister Andrew Robb and 20 senior businesspeople.
Border issues have been a long-standing headache between the two countries.
Indonesia, with its thousands of islands and shortage of maritime resources, is often used as a transit point by asylum seekers desperate to reach Australia's Christmas Island in hopes of starting a better life. Thousands board rickety fishing boats every year to make the often deadly journey, which typically crosses about 340 kilometers (210 miles) of open sea.
Abbott won the Sept. 7 election on the promise that he would stop the asylum seeker boats.
Indonesia has expressed concern over Abbott's "tow-back" plan, which involves the Australian navy intercepting and forcing back Indonesian fishing boats crowded with asylum seekers. Indonesian Foreign Minister Marty Natalegawa has warned that the move could breach the country's sovereignty.
On Monday, Abbott pledged "Australia's total respect for Indonesia's sovereignty."
Yudhoyono agreed that the two countries must work closely together to combat the problem.
"The solution is cooperation," he said, adding that specific details would be worked out at another forum between the countries. "Effective, precise and good cooperation."
Australian Immigration Minister Scott Morrison on Monday maintained his government's policy of refusing to say whether any boat had been turned back to Indonesia since the new administration took power on Sept. 18.
- AP