Border issues have been a long-time headache shared by the two countries.
Indonesia 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 took office two weeks ago after winning 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. Indonesia Foreign Minister Marty Natalegawa has warned that the move could breach the country's sovereignty.
On Friday, a boat thought to be carrying more than 100 asylum seekers from the Middle East sunk off West Java's Sukabumi district after being hit by high waves. The search continued Monday for dozens believed missing after 35 survivors were rescued. The exact number of people aboard the boat was unknown due to the lack of a manifest.