LONDON— Norwegian Air Shuttle AS A has rebuffed a takeover bid by British Airways parent IAG, as the battle over the lucrative trans-Atlantic market intensifies.

International Consolidated Airlines Group SA, as IAG is formally known, said Friday it had made a takeover offer, after disclosing in April a 4.61% stake in the Scandinavian budget carrier.

“We are looking at all our options,” ​IAG Chief​ Executive Willie Walsh said Friday after Norwegian rejected its approach, which was made in recent weeks.

London-based IAG, which posted strong first-quarter earnings Friday, didn’t give the value of the takeover offer. As of Friday, Norwegian’s market value, including debt, stood at 33.4 billion Norwegian krone, or $4.2 billion.

In a statement, Norwegian said IAG had made two conditional offers, both of which were unanimously rejected. The Oslo-based airline’s board affirmed its support for current business plans.