* Insulting material seen by Indonesian trainer - reports
* Often uneasy military ties slowly rebuilding since 1999
* Indonesia and Australia cooperate on counterterrorism training (Recasts, adds Indonesian defence minister comment)
By Fergus Jensen and Jonathan Barrett
JAKARTA/SYDNEY, Jan 4 (Reuters) - Indonesia's military acted alone when it suspended cooperation with Australia's armed forces last week, Indonesian officials said on Wednesday, after what media described as insulting teaching materials were found at a base in Western Australia.
A spokesman for Indonesian President Joko Widodo said there had been no discussion of the suspension with the president and the issue had been exaggerated.
"This was not a decision of the president," spokesman Johan Budi told Reuters.
Ties with Australia were "just fine", said Defence Minister Ryamizard Ryacudu, adding that he only learned about the matter on Wednesday.
"We need to look at this properly first, not just from one side," he added.
Australian Defence Minister Marise Payne said only some activities had been "postponed".
Military cooperation between the two countries, which ranges from counterterrorism cooperation to border protection, was suspended for "technical reasons", a spokesman for the Indonesian National Armed Forces (TNI) told Reuters.
"All forms of cooperation have been suspended," Major General Wuryanto said.
"There are technical matters that need to be discussed," Wuryanto said, referring to the training material seen at an Australian military base, but he declined to elaborate.
It was "highly likely" cooperation would resume once those issues were resolved, Wuryanto said.
Concerns were raised by an Indonesian military officer late last year about some teaching materials and remarks at an army language training facility in Australia, said Payne.
"As a result, some interaction between the two defence organisations has been postponed until the matter is resolved. Cooperation in other areas is continuing," she said.
A spokesman for Indonesia's Foreign Ministry did not answer telephone calls or respond to a written request for comment.
"FOUNDING PRINCIPLES INSULTED"
Indonesia last suspended military ties with Australia in 2013 over revelations that Australian spies had tapped the mobile telephone of then President Susilo Bambang Yudhoyono.
Australia stopped joint training exercises with Indonesia's Kopassus special forces after accusations of abuses by the unit in East Timor in 1999, as the territory prepared for independence three years later.
Jakarta and Canberra resumed military ties, saying cooperation on counterterrorism became imperative after the 2002 bombing of two nightclubs on the resort island of Bali that killed 202 people, including 88 Australians.
With ties gradually warming, the first joint training exercise on Australian soil since 1995 was staged in the northern city of Darwin in September last year.
But relations again became strained after an Indonesian special forces trainer saw training material that insulted the country's founding principles of "Pancasila", which include belief in god, the unity of Indonesia, social justice and democracy, Indonesian newspaper Kompas said.
The suspension of cooperation took effect in a Dec. 29 telegram sent by Indonesian military chief Gatot Nurmantyo, it added.
Australian media said the offensive material was found at Campbell Barracks in Perth, but officials at the army base declined to answer questions when contacted by Reuters.
The offices of Australian Prime Minister Malcolm Turnbull and Foreign Minister Julie Bishop declined to comment.
The suspension of military ties was met with skepticism by many analysts, who expect the relationship to be quickly mended.
A suspension could threaten Australia's controversial policy of turning back asylum seekers, said Greg Barton, a professor of global Islamic politics at Deakin University, but he doubted intelligence sharing would stop.
"Everyone acknowledges that the threat of an attack is the highest it has ever been," he added.
Visiting Jakarta in October, Bishop said it was "utterly essential" for Australia and Indonesia to share information and work closely to guard citizens against terrorism.
Unrest in Jakarta forced Widodo to postpone a trip to Australia planned for November that had aimed to discuss defence ties, among other subjects.