The chain, owned by US giant Walmart, reported a 2.9 per cent fall in like-for-likes sales in its fourth quarter.
The figures represent a tenth consecutive quarter of sales declines but mark an improvement from the previous two periods, which saw Asda post its worst ever sales falls of 7.5 per cent in August and a 5.8 per cent decline in November.
Clarke said: “We are encouraged by the early signs of our customers responding positively to the hard work that’s been happening in our stores throughout 2016, which saw us welcome over 140,000 customers back to Asda this last quarter.
“We are putting customers first and have sharpened our prices, improved our ranges and availability, all with friendly service.
“While we have a lot to do, it is great to see our colleagues, who really make the difference, engaged in this change in doing what’s right for customers.”
Clarke, who took up the reins on 11 July after being parachuted in to replace previous boss Andy Clarke, has slashed the prices of everyday items as he attempts to arrest falling sales.
Asda announced in September that it was lowering thousands of prices on everyday favourites by an average of 15 per cent, with items such as beef, chicken and sausages all becoming cheaper. The move has also seen Asda improve the quality of its own-brand ranges.
The turnaround comes as Asda fights back having lost out recently in a brutal price war that has engulfed the sector.
Walmart chief executive Doug McMillon said: “In the UK, we faced some challenges this past year and we’re addressing these with urgency.
“We’re encouraged comp store sales improved during the fourth quarter.
“I visited stores in the market a few weeks ago and the team has us pointed in the right direction.”
A recent supermarket consumer satisfaction survey carried out by Which? saw Asda come a worst possible ninth place, as well as joint last in the online rankings.
While Asda was seen by consumers as being generally good value, its food quality was rated in the Which? survey as average.
All of the so-called “big four” supermarkets – Tesco, Asda, Sainsbury’s and Morrisons – have suffered as German discounters Aldi and Lidl have gobbled up market share.