Some dairy farmers have said they face going out of business if prices they receive for their products do not rise.
They have held protests at supermarkets to show their frustration that they are currently paid less than the cost of production.
Asda has said it will begin paying 28p a litre for milk from Monday.
Dairy farmers currently receive about 19p a litre for milk, well below the cost of production at about 27p.
Asda confirmed on Friday that it had told Dale Farm, its Northern Ireland supplier, that it will increase the price it pays to 28p a litre.
It said this would "assist our farmers during the current crisis".
Ian Marshall, the president of the UFU, said Asda's move was something farmers were "glad to see" and hoped other retailers would follow.
But he warned that the situation remained "dire" for those in the dairy industry.
"It's a starting point for us," Mr Marshall said.
"What we're seeing is a move in the right direction.
"We just hope it's something that it can roll out to other products, not just milk."
Mr Marshall said farmers accept that they need to "strive to produce as efficiently as possible".
Asda has said that the cost of paying more for milk will not be passed on to its customers and retail prices will remain at their current rate.
A decision by supermarket chain Asda to increase the price it pays for milk is a move in the right direction, the Ulster Farmers' Union (UFU) has said.