Javad Owji told reporters that more 1,650 gas stations, which amount to over 30% of the pumps in the country, remain in service.
Earlier, the head of the Gas Stations Union said the software error has knocked fuel rationing system in Iran off course and that offline fueling system at non-subsidiary prices has not been affected.
Assadollah Gholizadeh told ISNA news agency on Monday that officials are working to tackle the software problem.
Gholizadeh also asserted there are no shortages of supply and advised motor vehicle users not to rush to the operational gas stations for a few hours if they do not urgently need to refuel.
He also dismissed reports that there disruption is a prelude to an increase in fuel prices.
Iranian Deputy Oil Minister Jalil Salari also assured the problem will be resolved within hours.
A group dubbed ‘predatory sparrow’ claimed responsibility for the hacking.