Due to maintenance work, the refinery had been operating at 50-55% capacity, affecting all of MOL's products.
"MOL remains committed to maintaining security of supply from our own products, however securing full market supply can not be ensured without the ramp-up of product imports in the current environment," the company added in its statement.
On Monday MOL said that it faced a partial shortage of fuel stocks across almost its entire network of filling stations over the weekend as many people started panic buying and stockpiling.
The company said that the primary cause of the fuel shortage was a lack of imports.
Foreign players have cut fuel shipments to Hungary since the government capped the price of petrol and diesel at 480 forints ($1.22) a year ago.
The price cap currently applies to drivers of privately owned vehicles, farm vehicles and taxis and is set to expire at the end of December.
The government has said it would decide whether to extend the measure based on information from MOL on whether the company is able to ensure supply. The government did not reply to Reuters questions on Monday and Tuesday.
($1 = 394.2500 forints)
(Reporting by Anita Komuves; editing by Jason Neely)
