Deutsche Lufthansa AG boss Carsten Spohr has crossed swords with Michael O'Leary, his counterpart at Ryanair Holdings, vowing to defend the German carrier's domestic market from further encroachment from budget airlines despite Mr. O'Leary's assurances that the business can only shrink.

Mr. Spohr said Lufthansa's current revamp of its short-haul operations will protect its market share, despite having lost ground in Europe to the likes of Ryanair and U.K. budget carrier easyJet PLC for years.

"Our competitors are realizing that Lufthansa Group won't be squeezed out of its home market," Mr. Spohr told The Wall Street Journal in a recent interview.

Mr. O'Leary isn't so sure.

"The legacy carriers' model in Europe has failed, it is over," Mr. O'Leary said in a separate interview with The Wall Street Journal.

The war of words comes as Europe's flag carriers continue to struggle to bring down costs fast enough to compete effectively with budget airlines whose passenger numbers in Europe continue to grow inexorably. Lufthansa reshuffled responsibilities on its management board earlier this month as it looks to make EUR500 million (US$560 million) in annual savings by 2019.

Passenger numbers at Ryanair, which has no long-haul business, rose 6% to 86.4 million passengers in 2014 compared with a 1.3% rise to 106.0 million for Lufthansa and sister carriers Swiss and Austrian Airlines, a figure which includes long-haul and short-haul flights.

Mr. O'Leary said that in five to 10 years, budget airlines will have squeezed out legacy network carriers and operate nearly all flights within Europe.

Discount carriers will restrict former monopoly airlines like Lufthansa, Air France and KLM to servicing their principal airport hubs that connect long-haul passengers with short-haul flights in Europe, he said.

Even there, Ryanair has an opportunity to help connect long-haul passengers to secondary European destinations. "As we begin to expand into more primary airports, you can have short-haul feed at a fraction of the cost of your own short-haul feed", Mr. O'Leary said. "Use us, use easyJet. It is inevitable this will happen in the next number of years."

So far, none of Europe's major network carriers has signaled interest in taking up the discounter up on its offer.

Ryanair has made the German market a focus for growth as part of its own reorientation to serve more primary airports and lure business travelers. The Irish carrier has begun operating intra-German flights from Cologne, where Lufthansa's Germanwings budget unit is based.

Mr. Spohr remains sanguine. Lufthansa's new low-cost airline will become Europe's third largest, dominating its home markets of Germany, Austria and Switzerland.

Lufthansa and Germanwings will be profitable this year on their European networks, demonstrating the resilience of their business which is deterring Ryanair from setting up at Lufthansa's hubs in Frankfurt and Munich, he said.

That is not to say Lufthansa is ruling out partnerships for its new budget unit Eurowings, which aims to have lower costs than Germanwings, though Mr. Spohr declined to give details

Germany's largest airline last week also unveiled a restructuring aimed at cutting costs and will give Eurowings more independence from Lufthansa's day-to-day operations.