Walmart International boss Judith McKenna said the United States chain is considering an initial public offering (IPO) for its United Kingdom subsidiary, but said it was "not rushing into anything".
In the first discussions of Asda's future since the U.K. Competition and Markets Authority torpedoed the proposed merger with Sainsbury's in April, McKenna suggested that preparations for the IPO would "take years".
Gary Carter, GMB national officer, said: "GMB's tens of thousands of Asda members have had enough uncertainty - they need to know that their futures are safe and secure".
Judith McKenna, chief executive of Asda's owner Walmart, has told staff such a listing is being considered.
He said new services were as important to customers as price and so the group would be testing ideas including same-day grocery deliveries and more use of technology such as scanning goods and paying via mobile phone in stores.
Walmart has revamped its global portfolio by selling a majority stake in its Brazilian business and acquiring a majority interest in Indian e-commerce leader Flipkart Group in its biggest-ever deal.
She added: "Walmart does not have a one-size-fits-all approach to operating its global markets, but a consistent focus on strong local businesses powered by Walmart".
Asda CEO Roger Burnley told staff to "forget the language of Plan A and Plan B", adding that Asda's one clear strategy "requires momentum in the short term, growth in the medium-term and sustainability in the long term". He said Asda planned to plow a further 80 million pounds in cutting prices for the rest of the year, which Monteyne called a "substantial price investment".