His comments came as Indonesia's military chief described the curriculum taught at a Perth army base as "too painful to explain", adding that it discredited Indonesia's military, its people and even its ideology.

President Jokowi, as he is popularly known, said the decision to halt defence co-operation had been conveyed to him and he ordered that it be handled by Commander-in-Chief General Gatot Nurmantyo and Defence Minister Ryamizard Ryacudu.

"Indonesia and Australia agreed to mutually respect and appreciate each other and not to get involved in each other's internal affairs," he said. "I believe we agreed to that."

President Jokowi said the relationship between the two countries was still in good condition: "Only maybe at the operational level this is what needs to be conveyed for the situation not to heat up."

Asked how long the suspension would last, he said: "This matter needs to be cleared up first because even though it is at the operational level it is a matter of principle."

Prime Minister Malcolm Turnbull welcomed the President's remarks in a statement issued on Thursday night.

"The President and I share a firm commitment to continue to build on the close relationship between our countries, based on common interests and mutual respect," Mr Turnbull said in the statement.

"I acknowledge and value President Widodo's commitment to the strategic partnership between our two countries and value our personal friendship."

A press statement issued by chief security minister Wiranto said the postponement of defence cooperation related to the Special Forces Australia language training program only.

"Military ties have not been completely severed as reported by many media outlets," he said.

"It is temporary in nature. It will resume once Australia has taken steps to finalize the case. This matter will not disrupt the bilateral relations between two countries that has been going well."

"With this explanation hopefully will be no more reporting that causes confusions and disrupts the bilateral relationships between the two countries."

At a news conference explaining Indonesia's decision to put defence co-operation between the two countries on ice, General Gatot said what was taught was "unethical" for a friendly country.

"It is too painful to explain so I won't explain," General Gatot said.

General Gatot said every soldier was taught to love their country's ideology so they were ready to sacrifice their lives when they faced the enemy.

He was upset over teaching on topics such as past Indonesian soldiers, East Timor, that West Papua should be independent and "Pancagila", a spoof of the state ideology of Pancasila which suggests its five principles are crazy.

"That's not right. Because of that I pulled back the teacher and I suspended it," General Gatot said.

He said Chief of the Australian Defence Force, Mark Binskin, was his "good friend", and had written a letter of apology and said he would fix the curriculum.

Air Chief Marshal Binskin told him he would investigate, send the Australian Army chief to Indonesia and extended the apology to General Gatot and the Indonesian Army Chief.

"Since he is my best friend, I also sent him a letter. I thanked him for the apology and we suspended the program and there will be a conversation after the investigation is complete," General Gatot said.

Australian Defence Minister Marise Payne said an Australian Defence inquiry into the offensive material, under way since late November, was "close to finalisation".

Senator Payne said Indonesia had not taken part in some planned events because of the dispute but negotiations about the country's involvement in a multilateral military exercise planned for next month were ongoing.

She had only written to her Indonesian counterpart about the dispute for the first time this week despite becoming aware of the concerns in November.

The Indonesian military confirmed to Fairfax Media that joint navy patrols would continue.

In a speech last month, Commander Gatot also said when he became Commander-in-Chief he put a stop to Indonesia sending top-ranked army officers to Australia to study, to prevent Australia from "recruiting" them.

He also raised concerns about the US Marines that rotate through Darwin, pointing out the close proximity to West Papua and Indonesia's giant Masela gas block.

General Gatot said there were 1500 US Marines in Darwin, which would soon increase to 2500.

"I, as TNI (Indonesian military), have to wonder what it's all about," Commander Gatot said.

"Why not in the Philippines? They have a base there. No problems, but it's Darwin," he said in the speech which has been posted on YouTube.

In 2011 Indonesia sought an urgent explanation from then Prime Minister Julia Gillard about plans to station US Marines in Darwin, questioning the need for a military build-up on the country's doorstep.

Indonesia has long been suspicious of Australia having hidden motives towards West Papua after its intervention in East Timor, despite it formally recognising Indonesia's sovereignty over the province in the 2006 Lombok Treaty.

Senator Payne denied Australia had recruited Indonesian military officers as spies or agents of influence

She said the US Marine rotation had been under way for some years.

"I have in fact discussed the Marine rotation with my counterpart in a number of meetings in the past and have had no concerns raised with me," she said.

"Let's be clear ... it's not a new occurrence and it is something which has been very important in the region."

With Amilia Rosa and Karuni Rompies

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