Asda - traditionally the cheapest among major fuel sellers - said drivers would pay no more than 126.7p a litre for petrol and 133.7p for diesel at its 223 forecourts.
That is 5p cheaper than average UK pump prices yesterday, of 131.90p for petrol and 139.04p for diesel.
Morrisons said it would be bringing down the price of both its diesel and unleaded by up to 2p a litre “at the majority of its sites”.
Sainsbury’s said it would cut “up to 3p a litre” from petrol and diesel at all its forecourts, while Tesco will bring its petrol and diesel prices down by “up to 2p a litre”.
Asda’s move surprised the Automobile Association, which comes amid uncertainty in the market, with the price of oil increasing by $2 a barrel yesterday.
AA spokesman Paul Watters said: “Asda’s pump price cut is a bold move. Although it reflects a fall in the wholesale price of petrol during last week, the continued disruption of Libyan oil production continues to leave the market volatile and unpredictable.
“The average price of petrol in the UK has hovered around the 132p-a-litre mark since mid October, making 126.7p a very good price.
“Unfortunately, other towns without Asda influence will not be so lucky.
“Even so, there will be some independent retailers who will take the opportunity to seize a local advantage. Drivers should keep an eye on the price boards.”