The Irish airline Aer Lingus is most profitable in a group that includes British Airways and Iberia of Spain.
Willie Walsh, chief executive of Aer Lingus's mother, International Consolidated Airlines Group (IAG), said the Irish company had done a "good job" to prevent Ryanair's competition.
He told Sundays at the Aviation Club UK dinner in Dublin that Aer Lingus was the "most profitable" in the group.
Mr. Walsh, former director of Aer Lingus, warned that some airlines could fail this year.
"We will see that some of these airlines are disappearing," he said, referring to turbulence that hit the sector in recent months.
He said, however, that Norwegian Air International, which plans to reduce its Dublin base as part of a series of measures to save € 200 million this year, is unlikely to be one of them.
IAG holds a 4.6 percent stake in Norwegian, but Mr. Walsh rejected speculation that it would be sucked into a bidding war for the troubled airline.
"I have been very clear that if we do not proceed to a full acquisition, we have no interest in retaining it," he said about the shares of IAG in Norwegian. "We are not going to start a bid war."
Mr. Walsh said he liked "what" Norwegian had done, but he wondered if the Boeing 787 vessel used was the right one.
Norwegian, which has an Irish airline license, offers cheap flights from Europe to North America, including services from the Republic to the US.
However, the courier came into difficulties this year when costs such as fuel increased and competition on the European air travel market was intensified. It plans to reduce the number of vessels flying from Dublin in September with the potential loss of 150 jobs as part of the cost savings plan.