The retailer is trialling a new partnership with Uber Eats to give customers delivery in as little as 30 minutes.
When using the scheme, customers can pick from more than 300 own-brand Asda products including fruit and vegetables, ready meals and drinks.
These items can be ordered via the Uber Eats app and will be picked up and delivered on the same day.
This is currently being tested in two stores, Pudsey Leeds and Barnes Hill, Birmingham.
There is no minimum spend for customers using the service and items will be delivered contact-free.
Vice president of online grocery at Asda Simon Gregg said: “We’re pleased to be partnering with Uber Eats to trial a rapid grocery delivery service for customers in Leeds and Birmingham.
“This will give Asda customers more choice in how they shop with us and offer yet another way to quickly and conveniently get their favourite branded and own-brand products delivered to the doorstep.
It has now been brought back into action and can now be used by shoppers again.
A Tesco statement said: “As you know, we suspended Delivery Saver payments in April, which allowed us to support 580,000 vulnerable customers with 1.1million orders.
“We couldn’t have done this without your patience and understanding. We’re now planning to restart Delivery Saver plans from July 1.”