World Trade Organization members have demanded compromises from the EU and Britain to ensure foreign businesses do not lose market access in post-Brexit trade.
At a meeting of the WTO's Goods Council, 15 countries - including the US, India, Australia and Canada - raised concern over the so-called Tariff Rate Quotas (TRQs) that will be in place after Brexit.
Under WTO rules, nations use TRQs to set a threshold at which foreign goods can be imported at reduced tariff rates.
Non-European nations have warned that their producers could lose access to both the British and EU markets.
They fear that EU quotas will be soaked up British imports, while British quotas will be filled by imports from the EU.
"We will be quickly crowded out and face a loss of access to both markets," the US said in a statement delivered to the WTO meeting.
New Zealand agreed that it was "hard to see" how WTO members from outside Europe "would have much realistic chance of accessing these quotas".
New Zealand also called on London and Brussels to create quotas "explicitly preserved for other WTO members to maintain our existing levels of access, or substantially expanded (quotas) to account for the large bilateral EU-UK trade."
Australia said its businesses with licenses to export agricultural products to the EU under the existing quotas system had already suffered "significant commercial disruptions" because of the uncertainty surrounding the system after Brexit.