From Tuesday Sainsbury's is cutting its petrol and diesel prices by up to 2p a litre.
Earlier, Asda announced a 2p reduction, saying that from Tuesday anyone filling up at its pumps would pay no more 130.7p a litre for petrol and no more than 134.7p a litre on diesel.
Asda's petrol trading director Andy Peake said: "We're giving our customers the opportunity to fill up their cars with lower-priced fuel, putting much-needed cash back in their pockets.
"Our national price cap benefits everyone across the country, meaning that no-one filling up at Asda will be forced to pay a premium for their fuel because of where they live."
Sainsbury's head of fuel Richard Crampton said: "We know that fuel is a big part of many customer's weekly budget so we're keen to do anything we can to help."
AA president Edmund King said: "Drivers will welcome the latest fuel price reductions at the pumps. Prices of petrol and diesel both crept up around 1p a litre last month.
"Our June fuel price report revealed that retailers had on average this year been charging at least a 1p per litre extra on diesel. Hence we believe that all retailers should look to cut fuel prices to reflect the market price at the pumps.
"Yet, when they sell it to drivers, diesel is typically around 4p more expensive than petrol. The AA advices that diesel prices vary locally more than petrol so drivers should search out diesel-friendlier forecourts."