The move by both companies is likely to be to encourage motorists to fill up at their stations before going into their stores for some last minute Christmas shopping.
Asda was the first to announce fuel price cuts, with the company saying that it was to cut up to 2p off a litre of petrol and 1p off a litre of diesel from today.
Thanks to these reductions, customers who fill up their car’s tank at Asda will pay no more than 126.7p a litre for petrol and 134.7p for diesel.
Andy Peake, Asda’s petrol trading director, commented: "With Christmas just around the corner, and finances tighter than ever, we are pleased we can do our bit to make our customers’ hard-earned cash go a little further."
He added: "Other Scrooge retailers should share the Christmas spirit and follow our lead."
Well another retailer did follow Asda’s lead, with Tesco afterwards announcing that it too was to drop the price of petrol by up to 2p a litre and diesel by up to 1p a litre – the same price cuts as Asda is offering.
In a statement, Tesco said: "As Britain’s biggest fuel retailer this means more motorists can make savings and earn Clubcard points at Tesco’s 498 petrol filling stations than at any other fuel retailer."
Peter Williams, head of external affairs at the RAC, was pleased with the Christmas fuel cuts, adding: "Cheaper fuel is something motorists will widely welcome and comes ahead of both last-minute Christmas shopping this weekend and the rush on the roads next week.
"The wholesale price of fuel is at its lowest rate since early November, so we hope other retailers pass on a similar saving. The RAC will continue to campaign on motorists’ behalf into 2014 to help ensure prices are fair."
Although both Asda and Tesco are reducing the price of fuel from today for the Christmas run-in, supermarket rival Sainsbury’s has stated that it will not be following suit, although saying that it "always remains competitive".
In addition, Morrisons has revealed that it will not be cutting the cost of fuel but would "remain competitive in every area we operate".
Petrol price reductions by Asda and Tesco follow the recent good news for motorists from Chancellor George Osborne’s Autumn Statement, in which he said that fuel duty would be frozen until 2015, with a planned rise in 2014 scrapped.