Both Joko Widodo and Tony Abbott are said to be keen to reset the Indonesia-Australia relationship after friction over asylum-seeker boats and spying allegations.
Indonesia's new president was sworn in on Monday, giving a vision of Indonesia rising as a mighty maritime power.
The former Jakarta governor's ascent was met with jubilant celebrations in the capital, where the 53-year-old has cemented his reputation as a reformist and man of the people.
He made time in the evening to briefly meet visiting foreign leaders including Mr Abbott.
Joko Widodo has encouraged open lines of communication with Australia.
"If we have problems ... speak to my ambassador because for me, communication is important," Mr Joko said.
Mr Abbott said he expected the relationship to go "from strength to strength".
"I'm very encouraged by everything President Jokowi has said up to now, I really am encouraged."
He acknowledged the long importance of the relationship to Australia, noting his Liberal predecessor John Howard had attended the inauguration of Susilo Bambang Yudhoyono.
Earlier, he remarked on the "wave of confidence" he witnessed in Indonesia during his brief stay.
"I'm very encouraged by everything President Jokowi has said up to now, I really am encouraged," he told reporters before the president's inauguration, using the Indonesian leader's nickname.
In his maiden speech, Mr Joko detailed his vision of the archipelago as a great maritime nation in line with the navy's motto: "in the sea we are victorious". In his evening speech to thousands of citizens at the national monument, known as Monas, he celebrated the everyday Indonesians.
He asked everyone from street vendors to nurses to work harder for the nation.
"It's impossible for this big nation to become a strong country, to become a great nation, if we're lazy," he said.
After meeting with Mr Abbott, Mr Joko told reporters the main issue discussed was his invitation to the G20 summit in Brisbane.
He was still unsure if he'd attend.
"I don't know because I have no cabinet yet," he said.
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