Indonesia appeared to back down Thursday from a decision to suspend all military cooperation with Australia in a row over teaching materials, with a senior minister saying only language training had been put on hold.

The Indonesian military said Wednesday that military cooperation with Canberra, including joint exercises and exchange programmes, had been put on ice last month after teaching materials deemed offensive to Jakarta were found at an Australian army base.

The row erupted after a visiting Indonesian officer raised concerns about the materials at a language training facility in Perth.

Indonesia's military chief General Gatot Nurmantyo told reporters it involved "unethical stuff" which "discredits Indonesia and its military, even the nation's ideology".

He said it concerned East Timor -- which seceded from Indonesia after a bloody occupation -- the Papuan region's independence movement and the nation's founding philosophy "Pancasila", all deeply sensitive topics for the Indonesian military.

But following the military's announcement, leaders of both Australia and Indonesia publicly insisted ties were strong before Indonesian Security Minister Wiranto announced Thursday he was giving a "clarification" after receiving information from Nurmantyo.

The military "has temporarily suspended cooperation in language training," said the minister in a statement, adding it was due to "a small incident that has offended our dignity as a nation".

But he said Indonesia was not "completely stopping all cooperation", contradicting the earlier military statement. Indonesian and Australian forces cooperate on a range of issues from border protection to counter-terrorism.

"The suspension is temporary and will be resumed after Australia clearly takes measures to resolve the matter," he added.

- 'Relationship strong' -

The Australian Broadcasting Corporation also broadcast footage Thursday of Nurmantyo giving a lecture in November, voicing fears Canberra was trying to recruit soldiers sent to Australia for training.

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"Every time there is a training programme -- like recently -- the best five or 10 students would be sent to Australia. That happened before I was chief so I let that happen," he said in translated remarks, according to the broadcaster.

"Once I became chief commander of the national forces, it (the students being sent) did not happen again. They will certainly be recruited."

Australian Defence Minister Marise Payne denied Canberra had targeted Indonesian soldiers to be potential agents.

She added that an investigation into the teaching materials that sparked the spat was almost complete and the government took the concerns seriously.

Despite the row, Indonesian President Joko Widodo said relations with Canberra remained robust.

"I think the relationship between Indonesia and Australia is in good condition, but perhaps on the operational level it still needs to be discussed so things will not heat up," he said.

But he added the dispute about teaching materials was "a matter of principle" that needed to be cleared up.

Australian Prime Minister Malcolm Turnbull later said that Widodo "and I share a firm commitment to continue to build on the close relationship between our countries, based on common interests and mutual respect.

"I look forward to this matter being resolved as soon as possible."

It is the latest tiff between the key allies and neighbours, whose relationship has been beset in recent years by disputes over Jakarta's execution of Australian drug smugglers and Canberra's hardline policy of turning migrant boats back to Indonesia.

Tensions also emerged over the role of notorious Indonesian unit Kopassus' part in human rights abuses in East Timor in 1999 as the then-Indonesian territory geared up for independence.