The ambassador recently met Australian Foreign Minister Julie Bishop for the first time since he was recalled, AAP reported.
President Susilo Bambang Yudhoyono last November was disappointed and recalled the ambassador following reports that Australia had spied on the president, his wife and his inner circle.
The ambassador quietly returned to Canberra this week, the first major sign of a thaw in diplomatic tensions between Australia and Indonesia, AAP wrote.
Kesoema and Bishop spoke over the phone upon his arrival, but on Wednesday went a step further when they met in person at parliament house in Canberra.
The talks were reportedly constructive and a significant step towards strengthening relations between the two countries.
Its hoped the ambassadors return can galvanise talks on a proposed code of conduct being negotiated by Australia and Indonesia and heal the diplomatic rift caused by the spying revelations.
Indonesia demanded Australia sign a code of conduct before it lifted a ban on high-level co-operation and started working together on people smuggling, defence and intelligence sharing.
Bishop has met her counterpart, Marty Natalegawa, nine times since the crisis began to try to broker an agreement, most recently in Mexico in April.
Despite sending a draft proposal of the code to Mr Natalegawa in December, a deal has not been finalised.
But in a significant step, Bishop and Natalegawa are scheduling dates for the next meeting between Australia and Indonesias foreign and defence ministers, known as a 2+2 dialogue.
Its expected these crucial talks could break the stalemate. President Yudhoyono recently expressed a desire to see an agreement reached by August, according to AAP.
(T.F001/C/F001/F001)
Editor: Aditia Maruli Radja
Copyright © ANTARA 2014
