Indonesia said Wednesday it has suspended military cooperation with Australia, reportedly due to training materials deemed offensive, in a fresh flare-up of tensions between the neighbours.

Cooperation including military exercises and education and exchange programmes were put on hold last month, said Indonesian military spokesman Wuryanto.

"Military cooperation with Australian forces has been suspended temporarily due to technical matters," the spokesman, who like many Indonesians goes by one name, told AFP.

Indonesian newspaper Kompas said it came after an instructor from Indonesia's special forces found training materials he thought were disrespectful towards his country and armed forces at an Australian academy during an exchange programme.

Wuryanto refused to confirm this, saying only that the suspension was due to several problems.

The neighbours are key allies but the relationship has had many ups and downs.

Ties sank to their lowest level in years under former Australian premier Tony Abbott due to rows about Jakarta's execution of Australian drug smugglers and Canberra's hardline policy of turning migrant boats back to Indonesia.

Indonesia had previously suspended military exercises with Australia, in 2013, due to allegations that Australian spies tried to tap the phone of then Indonesian president Susilo Bambang Yudhoyono, but they resumed the following year.

Wuryanto said the Indonesian military sent a letter to the Australian Defence Force on December 9 notifying them of the suspension.

"Hopefully the problem will be resolved soon," he said, adding that the Indonesian military was still in communication with the Australian forces.

It was the first serious row between the neighbours for some time, with relations having improved since Malcolm Turnbull became Australia's leader in 2015.