The meeting was held at around 07.00 p.m. local time shortly before Jokowi attended a folk party held by his supporters at the National Monument near the palace.
At his first time meeting with Abbott as the Indonesian President, Jokowi wore a long-sleeve batik, instead of suit and tie.
Abbott said earlier that his country wants Indonesias new President to be successful because a strong, prospering, democratic Indonesia has so much to offer to the world.
"President Jokowi now takes office with enormous goodwill - in his own country and in ours," he said.
After receiving Abbott, President Jokowi was scheduled to receive US Secretary of State John Kerry.
President Jokowi also received Malaysian Prime Minister Najib Razak and Singapore Prime Minister Lee Hsien Loong at the Merdeka Palace after his inauguration.
Jokowi was inaugurated as the seventh president and Jusuf Kalla as the twelfth vice president of Indonesia.
Jokowi and his running mate JK won the presidential election on July 9 after securing 70,997,833 votes, or 53.15 percent of the total 133,574,277 votes, while their rivals, Prabowo Subianto and his partner Hatta Rajasa, secured 62,576,444 votes, or 46.85 percent of the total. (A060/BSR/S012)