The discounter has developed two print ads that take a swipe at the supermarket's loyalty card, which was launched in October and is the first to "price match" against Aldi and Lidl.
The second ad features a mock-up of the card with the words "charge more and refund" in the style of the logo. A provocative message follows aimed at mocking the card.
It reads, "We believe Morrison’s loyalty scheme could have been given a name that actually explains what it offers. Just a thought.
"We don't price match. We price lead."
The discounter looks to be following in the footsteps of its fellow German discounter, Lidl, which launched a full-page print ad in October reminding customers that they could simply shop with Lidl instead of claiming back the cost of a more expensive shop through loyalty points.