LONDON— Ryanair Holdings PLC, Boeing Co. ’s biggest customer outside of the U.S., said it is walking away from talks with the U.S. jet maker over a potential new order for the 737 MAX in a dispute over pricing.

Boeing has pushed to catch up with rival Airbus SE on jet orders from airlines and lessors, after falling far behind in the crucial single-aisle category. The 737 MAX competes with Airbus’s A320 in that market, and Airbus capitalized on the MAX’s nearly two-year grounding to boost its market share.