(Adds comments from Widodo on free trade deal, background on two-way trade value)
By Harry Pearl
SYDNEY, Feb 26 (Reuters) - Australia and Indonesia said on Sunday that full military ties between the two countries had been restored, after Indonesia's military suspended cooperation in January because of "insulting" teaching material found at an Australian base.
Prime Minister Malcolm Turnbull made the announcement 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 said at a news conference in Sydney.
Widodo's visit to Australia comes less than two months after military ties were suspended, an event that sparked a minor diplomatic spat and led to an apology from Australia's army chief in February. Military cooperation between the two countries has ranged from joint training and counterterrorism cooperation to border protection. "insulting" material suggested that Indonesia's Papua province should be independent and mocked the nation's state ideology.
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.
While the primary focus of the visit was on security and economic issues, including the finalisation of a bilateral free trade deal by the end of the year, talks touched on tourism, cyber security and social links.
Widodo met Australian business leaders on Saturday, telling them that investor confidence in Indonesia was strong and reassuring them that Indonesia was a stable country in which to do business.
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.
Two-way trade between Australia and Indonesia was worth $15.3 billion in 2015-16, according to Australia's Department of Foreign Affairs and Trade.
Widodo said he was confident that a free trade deal would be finalised this year.
"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."
Widodo told The Australian newspaper this week he would like to see joint patrols with Australia in the South China Sea if they did not further inflame tensions with 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.
The leaders stopped short of announcing joint patrols on Sunday, but stressed the importance of resolving disputes peacefully and in accordance to international law.
"As maritime nations and trading nations, Australia and Indonesia are natural partners with common interests," Turnbull said.
Collaboration on counterterrorism, especially the return of foreign fighters from the Syrian and Iraq conflict zone, would continue, Turnbull said.