Abbott arrives three days after a boat packed with asylum seekers and bound for Australia sunk in Indonesian waters, killing 29 and leaving dozens more missing.
Before leaving Sydney on Monday, Abbott stressed the importance of the relationship between the neighbouring countries, which according to his office have two-way trade valued at 14.6 billion Australian dollars ($13.6 billion) a year.
"While Indonesia may not yet be our most important economic or security relationship, it is in many respects our most important relationship," Abbott said. "We will be covering a range of matters because this is an important relationship and it's important to get it right at the start of this new government."
Abbott is expected to meet with President Susilo Bambang Yudhoyono on Monday. He will be accompanied by Foreign Minister Julie Bishop, Trade Minister Andrew Robb and 20 senior business people.
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 crosses about 500 kilometres (310 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.