The supermarket chain sought to reassure shoppers that staff would be working around the clock to keep shelves stocked and said it would increase the number of delivery slots from 850,000 to 900,000 per week by the start of April to keep up with extra demand.
Asda will also roll out its partnership with Uber Eats to offer 30-minute deliveries from 200 stores from February.
Automatic counting technology is being used in Asda's busiest stores to control access and maintain social distancing.
The announcement comes after Tesco limited purchases of some items including toilet roll, hand wash, rice and eggs to prevent panic buying amid high demand.
Roger Burnley, Asda chief executive and president, said: “As Covid restrictions are tightened across the UK to protect our health, we will continue to do all we can to keep colleagues and customers safe in store as we have since the start of the pandemic.
“Our stores and distribution centres have proved to be highly resilient to the challenges of a national lockdown and we are confident that we can continue to deliver choice and value for customers in the weeks ahead.
"We are asking customers can play their part too by continuing to shop considerately and respecting social distancing when they visit our stores.”
Supermarkets' websites came under pressure this week after shoppers raced to book deliveries ahead of the third lockdown in England.
The major chains experienced problems with their apps and websites on Monday evening after Boris Johnson announced the tougher restrictions.
Tesco experienced issues with its online operations, Sainsbury's app went down temporarily and Morrisons and Ocado were forced to place shoppers in virtual queues.
Supermarkets enjoyed record sales of £11.7bn in December as shoppers stocked up for Christmas while bars and restaurants closed.
Data company Kantar said trade was boosted by the £4bn that consumers would normally have spent on food and drink outside the home over the festive season.
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