In front of Prime Minister Tony Abbott and other foreign dignitaries, including US Secretary of State John Kerry, Indonesia's seventh president quoted the first president, Sukarno, to challenge Indonesia to reassert itself as a maritime nation.

"I would like to call all fellow Indonesians to remember one thing stated by Sukarno: 'In order to build Indonesia into a strong, nation we need the spirit of courage to face the waves."

"As captain of the ship I would like to call everyone to come aboard the ship of Indonesia and to say to them we will sail and we will will face all storms and waves based on our strengths."

Addressing the question of foreign policy specifically, he suggested no change to Indonesia's historical approach, vowing to continue Indonesia's history of a "free and active" foreign policy "to be able to contribute to the world based on peace and just values".

However, he quoted the motto of the Indonesian navy "Jales Veva Jaya Mahe", which means "In the water, we are triumphant", and said that for too long it had turned its back on the "bays and straits and oceans".

"The time for us is to return to make Indonesia a maritime nation … to be as great in the oceans as our ancestors were in the past."

Indonesia, a nation of 13,000 islands, has long been concerned about its maritime sovereignty, partly because its navy is not well enough equipped to ensure it.

The comment reinforces his intention, expressed in a blunt warning to Mr Abbott in an exclusive Fairfax Media interview, to be "stronger" on maritime sovereignty, and to invoke maritime law against any Australian incursions.

Mr Abbott has made no comment about the question of borders and sovereignty, offering only very limited comments on Monday.

"Our relations with Indonesia are very important. This relationship matters. It's a strong relationship. The challenge is to make it stronger in the future that it has been in the past," he said.

"I'm very encouraged by everything that President Jokowi has said up until now – I really am encouraged. He's obviously a charismatic and inspirational figure ... I'm looking forward to Australia's opportunities to take part in the renewal and the reinvigoration of this important neighbour and partner."

Mr Joko's former bitter rival for the presidency, Prabowo Subianto, attended the inauguration ceremony at the parliament building in Jakarta furthering a process of reconciliation begun last Friday.

As Mr Joko acknowledged him at the beginning of his speech, Mr Prabowo stood and saluted, to rapturous applause from the 675 Indonesian members of parliament and dozens of dignitaries. The gesture suggests that, though Mr Prabowo's forces, which dominate the parliament, may still work as an opposition to Mr Joko's government, it may not be as obstructive as had earlier been feared.

Mr Joko said he would work to ensure that "every person in this great nation will get the help that they need from the government", even those living in remote areas.

Reaffirming his reputation as a president for the orang kecil, or ordinary people, he called on "fishermen, workers, farmers, bakso [meatball] sellers and street vendors, professionals, scholars, the military, police, businessmen" to work together.

"This is a truly historic moment for all of us to be able to work together, and to work and work and work," he said.

The inauguration, the first time in Indonesian history that one democratically elected president has handed over to another, has inspired great hope in the country of 240 million people.

Mr Joko promised, in his oath to to govern "to the best of my ability and in the most just and fair manner".

After the swearing in, outgoing president Susilo Bambang Yudhoyono vacated the president's seat, effectively swapping with Mr Joko.

The short ceremony will be followed by a parade down Jakarta's central thoroughfare, to the presidential palace, where Mr Joko has said he will live with his family. A series of bilateral meetings, including with Mr Abbott, are planned in the afternoon.