The supermarket said it would publish pump prices at each of its stations to enable people "to find the best value".
It comes as petrol prices have risen again, prompting concerns that cheaper prices at the pumps could be over.
The RAC motoring group welcomed Asdaʼs move but said it didnʼt believe it would make a difference to prices.
"Real competition is the key, and this is something we are sadly lacking at the moment," said the RACʼs fuel spokesman Simon Williams.
He added the group didnʼt believe "real change" was likely until an official price monitoring body was formed that could "fine companies that donʼt properly reflect significant downward wholesale market movements on their forecourts".
All petrol retailers are working with the Competition and Markets Authority (CMA) to set up a scheme to allow people to compare live fuel prices online.
An investigation by the watchdog found supermarkets, known usually to have cheaper fuel prices, had sought to increase profits from selling fuel, increasing their margins by 6p per litre on average between 2019 and 2022.
The RAC said with the cost of oil rising recently, retailers were "wasting no time" in passing on the higher wholesale costs to drivers.
The average cost of per litre of petrol is now £1.45, up by 1p since the start of July and nearly 2p since June.
But fuel prices on average remain much lower than last yearʼs record levels.
In July 2022, petrol prices hit £1.91 per litre in on average, while diesel rose to £1.99 in the aftermath of Russiaʼs invasion of Ukraine, which saw oil prices spike.
The RAC said while petrol prices had started to rise again in recent weeks, diesel had stayed the same at £1.46 per litre, ending a run of eight-months of falling prices.
Current prices mean filling a tank for a 55-litre family car costs around £80 for either fuel.
Luke Bosdet, the AAʼs spokesman on pump prices, said the jump fuel costs would impact holidaymakers using their vehicles this summer, but added "staycation road travel costs are way down" on last year.
"Where higher road fuel costs probably hurt most is potential spending at UK tourist destinations once again being siphoned off at forecourts on holiday routes," he added.
But the RACʼs Mr Williams said that the recent increase in pump prices were generally at independent forecourts, which make up the lionʼs share of filling stations, due to them being hit by much higher wholesale prices.
He said the UK was "not in the kind of upward price spiral we experienced last year", but added "it feels like the better times at the pump are over for the time being".
"The big question now is how quickly and how far pump prices rise," Mr Williams said. "Encouragingly, there has so far been very little upward movement from the big four supermarkets but only time will tell".
He said there was a decision for supermarkets over whether they would trade with smaller margins on fuel "that were closer to their longer-term averages", or whether they would look to make more money.
Petrol retailers to work on pricing scheme
Brent crude - the benchmark for oil prices - is around $85 a barrel, the highest level in over three months, which has been a driver in fuel prices rising.
Demand for oil has been outpacing supply, pushing prices up, and Saudi Arabia a major producer, voluntarily cut its production in July, and is expected to extend it.
Mr Williams said if oil producers continue to curb production then "bigger forecourt price rises could be on the cards".