Lawrence Hunt & Co Ltd - which operates 25 SPAR branches across Lancashire - said the outage is still affecting tills, credit cards and back office systems.
It means shoppers must pay with cash and stores are only selling 'essentials', such as milk and bread.
SPAR has not said when it expects its IT system to be fully restored, but said its computer technicians are "working as quickly as possible to resolve the situation".
The National Cyber Security Centre and Lancashire Police are also investigating the cyber attack.
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A spokesman for cyber force said: "We are aware of an issue affecting Spar stores and are working with partners to fully understand the incident."
More than 300 stores have been affected and those that remain open are only accepting cash due to debit and credit card payments not being able to operate.
A spokesman for Lawrence Hunt & Co said: "All stores are still affected - we have no tills and are offering essentials, but cash only.
"Post Offices are open as normal as they are on a different network.
"Our store teams are doing an amazing job in difficult circumstances."
Preston-based distribution partner James Hall & Company - which provides food to nearly 600 Spar stores across Lancashire and the North of England - has also been hit and its website remains down.
A SPAR spokesman said: "We are working to resolve this situation as quickly as possible.
"It is currently impacting stores’ ability to process card payments meaning that a number of Spar stores are currently closed to shoppers or only taking cash payments.
"We apologise for the inconvenience this is causing our customers and we are working as quickly as possible to resolve the situation."