Indonesia and Australia have restored full military relations, weeks after Jakarta suspended cooperation because of "insulting" teaching material found at an Australian army centre.

Australian Prime Minister Malcolm Turnbull made the announcement on Sunday alongside Indonesian President Joko Widodo, who arrived in Australia on Saturday for his first visit as president.

"President Widodo and I have agreed to full restoration of defence cooperation, training exchanges and activities," Turnbull told reporters in Sydney.

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Military cooperation between the two countries has ranged from joint training and counterterrorism cooperation to border protection.

It was suspended in January after an Indonesian officer saw references which he deemed derogatory to Indonesia's state ideology Pancasila in training materials used at a special forces base in the west Australian city of Perth.

A minor diplomatic spat ensued, followed by an apology from Australia's army chief in February.

Indonesia and Australia have a history of patchy ties, but both leaders were keen on Sunday to emphasise their commitment to a strong relationship.

"That robust relationship can be established when both countries have respect for each other's territorial integrity, non-interference into the domestic affairs of each other and the ability to develop a mutually beneficial partnership," Widodo said.

The two leaders also witnessed the signing of an agreement on maritime cooperation that includes strengthening maritime security and border protection as well as combating crime and improving efficiency of shipping.

"We have vested interests in the peace and stability in our region's seas and oceans, so we both strongly encourage the countries in our region to resolve disputes in accordance with international law which is the foundation for stability and prosperity," Turnbull said.

The leaders stopped short of announcing joint patrols, but stressed the importance of resolving disputes peacefully and in accordance to international law.

Collaboration on counterterrorism, especially the return of foreign fighters from the Syrian and Iraq conflict zone, would continue, Turnbull said.

Trade relations

While the primary focus of the visit was on security and economic issues, talks also touched on tourism, cyber-security and social links.

Two-way trade between Australia and Indonesia was worth $15.3bn in 2015-16, according to Australia’s Department of Foreign Affairs and Trade.

Following one-on-one talks, Turnbull said tariffs would be cut for Australian sugar and Indonesian pesticides and herbicides. He also praised changes to the export rules for live Australian cattle.

Widodo said he was confident that a free trade deal would be finalised this year.

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"I have conveyed to Prime Minister Turnbull some of the key issues," he said. "First, is the removal of barriers to trade, tariffs and non-tariffs for Indonesian products such as Indonesia’s paper and palm oil."

Earlier this week, Widodo told The Australian newspaper that he would like to see joint patrols with Australia in the South China Sea if they did not further inflame tensions with China.

China, which claims almost the entire sea region, irked Indonesia last year by saying the two countries had "overlapping claims" to waters close to them, an area Indonesia calls the Natuna Sea.