"Pancasila" is a term that refers to belief in one god, justice, unity, democracy, and social justice in Indonesia. The Australian Army renamed it "Pancagila" in laminated training materials, meaning "crazy."
Indonesia's military said on Thursday it received an apology from the Australian army over "insulting" material found at an Australian base late last year.
Indonesian army spokesman Colonel Bedali Harefa said the apology was submitted formally by Australia's Chief of Army, Lieutenant General Angus Campbell, while meeting Indonesian army chief General Gatot Nurmantyo in Jakarta on Wednesday.
"General Angus expressed deep regret and apology for the incident," said Harefa.
Indonesia's military partially suspended cooperation with its Australian counterparts in early January. The rift developed after an Indonesian military officer raised concerns in November about teaching materials for army language training at a special forces facility in western Australia.
Indonesian media reported that Pancasila, the state ideology based on five principles including a unitary state and belief in one god, was renamed "Pancagila," in effect calling it crazy in Indonesian, in laminated training materials.
Referring to the incident, Nurmantyo said in the statement that Indonesians have died to defend Pancasila. "Especially for the soldiers, it is very sensitive and it hurts us," he said.
The neighbouring nations, though close partners in areas such as trade and counter-terrorism, have long had a turbulent relationship.
Tensions have repeatedly flared over Australia's policy of turning back boats to Indonesia that are carrying asylum seekers from other countries. Indonesia's use of the death penalty, which Australia opposes, has also strained ties, particularly in 2015 when Indonesia executed two Australians for drug crimes.
In 1999, the relationship suffered one of its most serious blows after Australia led a UN military force into the former Indonesian province of East Timor following a bloody independence ballot.
Nurmantyo said the results of Australia's investigation into the Pancasila incident would be discussed with the defence and foreign ministers and then reported to President Joko "Jokowi" Widodo.
In January, Nurmantyo announced all military cooperation with Australia had been suspended but a day later, the top Indonesian security minister said the suspension applied only to language training.