"We are getting daily reports of remote stores struggling to supply basic goods," Aboriginal Medical Services Alliance chief executive John Paterson said.
"Some stores are running out of fresh food three days after their weekly delivery."
Mr Paterson said independent suppliers were struggling to get what they needed for remote stores.
"We want an agreed proportion of these essential goods set aside for the independent suppliers," he said.
"This can't be solved through donated goods. It needs a systemic response from government."
The coalition of health services, land councils, and other Aboriginal organisations also wants a 20 per cent, point-of-sale subsidy of essential food, cleaning and hygiene products, as well as winter bedding and clothing.
It says prices in some remote stores are already running 60 per cent higher than in the major supermarkets.
Source: Central Land Council/Facebook
"We understand fresh fruit, vegetables and meat are not in short supply in the southern states and distributors are actively planning to address current shortages in remote stores in central Australia," Central Land Council Chief Executive Joe Martin-Jard said.
"However, we believe subsidies on essential goods at point-of-sale coupled with a supply guarantee will make a huge difference."
"We urge the national cabinet to take action before it is too late because time is all remote Aboriginal communities have on their side in their fight against the virus."