Australia is among a number of countries seeking compensation from Britain and the EU over Brexit disruption.
The Australians were backed by other countries including New Zealand, the US, and Canada when they raised the issue at a World Trade Organisation meeting on Thursday.
The country's case concerns losses in what is a $366m (£193m) annual agricultural export trade with the European Union and Britain.
In a statement reported by the Australian Financial Review, an Australian official told the WTO: "Compensatory concessions should be provided to affected WTO members for loss of market access.
"Australia cannot accept the assertion by both the EU and UK that no compensation is required."
The dispute stems from Brexit-related problems faced by Australia's lamb and beef exporters.
The European Union only allows a limited amount of agricultural produce to come in from other countries at reduced or zero tariffs.
After that, tariffs are at such a level that exporting anything further is not viable.
When Britain leaves the EU, the quotas will be divided between them and the bloc but it has not yet been revealed what the permitted tariff rate quota (TRQ) will be.
There are conflicting ideas as to how the division will be calculated and, to make matters more complicated, the date for Britain's exit from the EU has shifted a number of times.
Australia and those backing it are worried that the calculations might leave them with a smaller export opportunity.
The Australian statement said: "It is clear the proposed modification to TRQs will lead to significant economic loss, by not only removing flexibility in where product is sent year to year, but also by rendering some TRQ allocations too small to be commercially viable."
Australia's Department of Agriculture said on its website: "The EU intends to 'split' existing agricultural WTO tariff-rate quotas between the UK and the EU-27 post-Brexit. This will include Australia's country specific quotas for beef, buffalo, sheep and goat meat, cheese, sugar and rice.
"The Australian government is currently negotiating with the EU and the UK seeking compensation as a result of the 'splits'.
"We are progressing potential changes to the administration of the EU's existing agricultural WTO tariff-rate quotas to prepare for a 'no deal' Brexit."