After initially placing limits on hand sanitiser and toilet paper after shoppers bought out existing supplies, the Coles and Woolworths chains have now introduced limits on the amount of other products, including rice, that shoppers can buy.

Depending on the store, there are now limits on other products including pasta, flour, paper towels and issues.

Other items like long-life milk and sugar were in heavy demand in Wagga on Saturday.

In a bid to help reduce panic and buying, the two major supermarket chains have also temporarily suspended their "change of mind" returns policies.

Instead of trying to return items they overbought, shoppers are being encouraged to consider donating the items to charity.

In a message to customers, Coles chief executive officer Steven Cain said employees and suppliers "have also been working as hard as possible delivering more products to stores every day and stocking shelves as quickly as possible".

"I would ask all customers to continue to respect and support our team members, particularly if a product is unavailable or the checkout queues are longer than normal," Mr Cain said.

Woolworths CEO Brad Banducci has issued a similar statement, also adding that the chain had introduced additional "deep cleaning" for its stores.