Jakarta has backed down over a suspension of all defence co-operation with Australia.
Senior cabinet minister Wiranto told reporters in Jakarta the suspension now only applied to language programs at special forces academies.
Less than 48 hours earlier, it had been across the board.
The suspension was triggered following an incident last November involving teaching materials causing offence to a special forces trainer at the Campbell Barracks in Perth.
The matter has been under investigation in Australia.
It's understood Army Chief Angus Campbell is being dispatched to Jakarta very soon to discuss the inquiry.
Labor MP Luke Gosling, who spent 13 years in the army and completed the language course at the Perth barracks in 1999, said his experience of the program had been excellent and respectful.
"Even during that difficult year for our bilateral relations and with the intervention in East Timor there was still a respect and desire for understanding maintained between the students and Indonesian lecturers," Mr Gosling told AAP.
He said the suspension of the language training was sad news because cultural understanding was essential for effective co-operation.
"It would be a shame if isolated incidents take us off a positive course," he said.
Deputy Prime Minister Barnaby Joyce said military co-operation between the two countries was important because "a threat to Indonesia was a threat to Australia".
"The terrorists that come into Indonesia are the same ones that are going to come into Australia," he told reporters in Canberra.
"I believe that this issue will be quickly put aside because it's in our interests to work together."
Indonesian President Joko Widodo said his country's relationship with Australia was in good shape.
"Indonesia and Australia have both agreed to respect one another and not to interfere in each other's domestic affairs," he told reporters in Jakarta.
"Although the issue lies at the operational level, this is a matter of principle."
Meanwhile, reports have emerged that Indonesia's military chief Gatot Nurmantyo hired a tourist boat in Darwin for a couple of hours to spy on US Marine landing bases.
"Australia is a continental country, (why does it need) marines?" he told Indonesian media website Viva.
