Abbott was on his first trip outside Australia since taking office four weeks ago. His Liberal National Party coalition defeated the Labor Party to win a majority victory in national elections.
People smuggling issues were high on the agenda for both countries during Abbott's visit, The Jakarta Post reported.
Australia's Department of Immigration estimated that up to July, 218 boats had already transported more than 15,000 asylum seekers to the country's waters this year. In all of last year, 278 boats transported about 17,200 people, a sharp increase from 134 boats that carried more than 6,500 people in 2010.
The Post reported Purnomo said many of the boats don't stop along Indonesia's coast, but cross Indonesian waters on their way to Australia's Indian Ocean territory of Christmas Island.
"We will track their routes to make sure that they haven't sailed from any of the islands in Indonesia and [we will] block their movements," Purnomo said.
He was speaking at the handing-over ceremony of the first CN-235 maritime patrol aircraft at the military base in Bandung, the capital of West Java province on the island of Java.
The aircraft are being built by the Indonesian state-owned aerospace business PT Dirgantara Indonesia. PTDI was awarded a contract in 2009 for three of the high-winged, turboprop CN-235 aircraft for use by the Indonesian navy.
Spanish aircraft maker EADS CASA and Dirgantara formed a joint venture, Aircraft Technology -- AirTech -- to develop the CN-235 aircraft in two variants for civil and military use.
PTDI will deliver the remaining two aircraft to navy in December and February.
Abbott was elected partly on a platform of getting tougher with asylum seekers arriving by boat and seeks more cooperation with Asian neighbors, including Indonesia, Malaysia and Thailand.
During his visit to Indonesia, Abbott reiterated his government's get-tough policy, including his party's Operation Sovereign Borders in which the 12 agencies involved in border protection are coming under the command of a single three-star military commander.
"The government of Australia takes a very dim view ... of anyone seeking to use our country as a platform for grandstanding against Indonesia. We will do everything that we possibly can to discourage this and prevent this," he said.
Details of any changes in people smuggling and asylum boat transfer policies between Australia and Indonesia are being discussed by Australian Immigration Minister Scott Morrison and his Indonesian counterpart, Djoko Suyanto.
An Indonesian Immigration spokesman told the Post Indonesia's immigration detention centers were overcrowded and a large number have been community houses.
"Apart from the migrants detained in detention centers, we also had around 2,028 migrants at community houses across Indonesia as of August," he said.
Indonesia's immigration offices across the country have been conducting public awareness campaigns to encourage local people to report suspected undocumented migrants in their neighborhoods, the spokesman said.
Australia came under harsh criticism last month after a boat of Indonesian asylum seekers floundered off Indonesia's south Java coast.
The tragedy left as many as 50 people, including 30 children, dead or missing, the Australian Broadcasting Corp. reported at the time.
Australian officials dismissed claims by asylum seekers that it took 24 hours for authorities to respond to the tragedy.
Australian coast guard officials said it sent out rescue vessels immediately it was contacted.