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.

They say it is to avoid people calling in sick, turning off their phones or simply failing to turn up for work.
Kabali, the star's latest movie, will be released in some 12,000 screens.
One of Asia's highest paid actors, Rajinikanth is considered one of the most bankable stars in India.
Even before its release, Kabali, a gangster drama, has raked in some $30m (£20m) in film rights sales. It will also be dubbed in Telugu, Hindi and Malay.
Excitement is mounting in southern India as the movie is set for release on Friday.
In Chennai and Bangalore, some companies have declared a holiday on Friday and given their employees free tickets for the film.
One firm said it had declared a holiday to "avoid piled up leave requests to the HR department".
A Bangalore-based company said it did the same to "avoid sick leaves, mobile switch offs and mass bunks".
Also:
In a career spanning four decades, the 65-year-old actor has starred in more than 170 films, most of them in Tamil language.

Bristol Crown Court heard Christopher Daldorph, 45, spent up to two hours a day over 14 years viewing the material.
Officers from the National Crime Agency (NCA) found 20 devices at his home in West Wick, Weston-super-Mare, when he was arrested in April.
One hard drive alone contained more than 150,000 images and videos.
Daldorph admitted nine counts of making indecent photographs and one count of possessing extreme pornographic images between November 2010 and April this year.
Passing sentence, Judge Geoffrey Mercer QC, said: "For over 14 years, as you admit, you have regularly set time aside to scour the darkest corners of the internet to find some of the more disturbing representations of child abuse available.
"This is in my judgment an extreme case of downloading indecent photographs of children, because of the volume of the material which you downloaded over a substantial time."
Christian Hall of the NCA said: "Daldorph was responsible for amassing hundreds of thousands of indecent images, some of them the most extreme possible involving very young children.
"Each of those involved a child being abused in some of the worst ways imaginable."
Daldorph, who had worked for the NHS for 17 years, was dismissed from his job after he was arrested.
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.
[NEXT_CONCEPT]
Businesses in southern India have given their employees the day off on Friday so they can attend screenings of a new film starring Tamil cinema superstar Rajinikanth.
[NEXT_CONCEPT]
A hospital radiographer, who downloaded more than a million indecent images and videos of children, has been jailed for two years and four months.