The chain says it will commit to paying 28p per litre for 100% of its liquid milk throughout its entire range.
It is less than the 30-32p farmers estimate it costs to produce each litre but the farming union welcomed it.
Asda's announcement comes after protests by dairy farmers at branches of Asda, Morrisons, Lidl and Aldi over the price they are paid for their milk.
The National Farmers' Union (NFU) said it was pleased Asda had recognised the "plight of the dairy industry" in its "hour of need".
The industry says a reduction in global demand for milk has led to an over-supply in the UK, creating difficult conditions for many dairy farmers.
Asda said it would increase the price it paid per litre to its milk supplier Arla from Monday, with the intention that it be passed directly on to farmers.
"Asda's origins are in dairy farming which is why we are acting in the best interests of our farmers and our customers by increasing the price we pay, introducing the Farmer's Marque label and not passing on any of the costs to customers - our retail price stays the same," he said.
It is not yet clear whether Arla, Britain's biggest milk co-operative, will pass on the increase in price to farmers.
Meurig Raymond, NFU president, urged Arla to ensure it passed the extra payment on "with immediate effect".
Asda previously announced a price cut of 0.8p per litre - taking the standard litre price to 23.01p for its UK members.
On Tuesday, Morrisons said it was launching a new milk brand which will see 10p per litre extra paid to farmers.
The Milk for Farmers brand, to be launched in October, means a four pint bottle (2.27 litres), which now sells for 89p, will cost an extra 23p.
The four main farming unions - the NFU, the NFU Cymru, NFU Scotland and the Ulster Farmers Union - held an emergency summit on Monday to develop an action plan to tackle falling milk, lamb and arable prices.
There have been days of protests by farmers including milk trolley challenges, blockades at distribution centres and even bringing cattle into supermarkets.
The average price paid to dairy farmers for milk across the UK is 23.66p - following a drop of 25% in a year.
The NFU said that currently Waitrose, Marks & Spencer, Tesco, Sainsbury's and the Co-op have arrangements where a farmer is paid a price above the cost of production for milk. Asda, Lidl and Aldi currently do not offer such deals to farmers.
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Asda is to increase the price it pays its milk supplier to "a level that will assist" farmers, the supermarket says.