Indonesia has suspended military cooperation with Australia, reportedly after training materials deemed offensive were found at an Australian army centre, officials said, in a fresh flare-up of tensions between the neighbours.

Indonesian military spokesman Major General Wuryanto said on Wednesday that cooperation has been suspended indefinitely, and that the decision was made after many matters were considered.

Although Wuryanto, who like many Indonesians uses one name, declined to give the exact reason for the decision, he said among the factors were reports of an Indonesian instructor saying that a "laminated paper" displayed at the Australian special forces base where he worked was insulting.

"This is not a protest ... we would like to establish a useful cooperation for the two nations based on mutual respect," Wuryanto told the AP news agency.

"Technically, it is not running well."

It was unclear what exactly in the materials had caused offence.

According to Indonesian media reports, the allegedly insulting paper displayed at the special forces base contained words that demeaned Pancasila, a set of vague principles that mandates belief in one God and unity among Indonesia's 250 million people.

Australian defence minister, Marise Payne said in a statement that Indonesia had informed Australia of the decision.

Some interaction between the two militaries "has been postponed until the matter is resolved. Cooperation in other areas is continuing," Payne said.

Payne said that the chief of the Australian defence force, Air Chief Marshal Mark Binskin, wrote to his Indonesian counterpart, General Gatot Nurmantyo, vowing that the matter would be addressed.

Shaky relationship

According to a report in Indonesian newspaper Kompas on Wednesday, the Indonesian military sent a letter to their Australian counterparts warning that cooperation could be suspended and then the head of the country's military, Gatot Nurmantyo, sent a telegram putting this into force on December 29.

It was just the latest dispute between the key allies, 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.

In 2013, Indonesia suspended military exercises with Australia due to allegations that Australian spies tried to tap the phone of then Indonesian president Susilo Bambang Yudhoyono. They resumed in 2014.

The latest military suspension is the first serious dispute between the neighbours for some time, with relations having improved since Malcolm Turnbull became Australia's leader in 2015.