Indonesia's Foreign Minister has complained about the lack of action in Australia against a protester who broke into its Melbourne consulate earlier this month and held up the West Papua flag.

Retno Marsudi said the protester who climbed onto the roof of the consulate to display a West Papua flag violated international law and should be prosecuted quickly.

She said Australia needs to "solve" the legal process around the January 6 protest at the consulate.

"The problem is the person who trespassed is shown in the picture, there is a photo, we already know his name," Ms Marsudi said.

"The question is why until now the person is still free."

The relationship between Indonesia and Australia was tested earlier this month when Indonesia's top general suspended military cooperation between the two nations, over "offensive" training materials at a Perth barracks.

The complaint, in November last year, prompted Australian Defence leaders to launch furious efforts to try to smooth relations with their counterparts in Jakarta.

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Sources familiar with the incident confirmed the "laminated material" concerned West Papua, an Indonesian province that has tried to seek independence from Jakarta, and which is perhaps Indonesia's most sensitive topic.

The Minister referenced the recent military spat between the two nations, saying that the countries have a high relationship intensity, and every now and again there is a problem.

She said both nations need to respect each nations' territorial integrity.