But for the retailers to do this, the monopoly lines companies that carry electricity to homes would also have to reduce their fixed charges.
"Those companies should be on notice that my patience is running thin," said Mr Hodgson in yesterday's speech. "I believe I am entitled to give notice."
He said the Government's first published request for a low fixed charge was now a year old.
The Electricity Amendment Act, giving the Energy Minister widespread powers to regulate, became law three months ago, meaning Mr Hodgson could now regulate.
"The industry should be aware that if fixed charges are regulated you will lose a significant amount of control over your own pricing methodology."
"It's your call, but I suggest you act quickly. It would be a pity if regulations have to be introduced just to deal with a few recalcitrants."
"I do not want to regulate. But if I must, I will. And once I take a decision to regulate, I will not reverse it."
Some industry sources have indicated that the unnamed lines companies Mr Hodgson was referring to in his speech are three of the smaller, largely rural lines businesses.
The idea behind the 10 per cent fixed charge stems from a fear that many small power users who asked companies for cheaper electricity had been told they were not wanted.
The 10 per cent fixed-rate tariff was a method of ensuring companies did not simply "cherry-pick" the big power users who paid bills on time.
Allowing companies to charge high fixed rates also removes any incentive for customers to conserve power, as the bulk of their power bill would bear no relationship to the amount of electricity used.
Power to the People Supplement
Energy Efficiency and Conservation Authority