LONDON—Ryanair Holdings PLC pledged Tuesday to sell its stake in Aer Lingus Group PLC in the event of an agreed takeover of the Irish flag carrier, in a last-ditch attempt by Europe's largest discount carrier to persuade the U.K.'s antitrust regulator that its 29% holding doesn't stifle competition.

The U.K.'s Competition Commission called on Ryanair in May to reduce its 29% stake in Aer Lingus because it said this was stifling competition on routes between the U.K. and Ireland and could prevent Aer Lingus from being sold.

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