"The board of Norwegian Air Shuttle (NAS) confirms that it has received two separate conditional proposals from IAG Group in relation to an acquisition of 100 percent of the share capital of NAS," it said in a statement.
"These proposals were reviewed in conjunction with NAS' financial and legal advisers, and were unanimously rejected on the basis that they undervalued NAS and its prospects."
In a presentation to investors on Friday, IAG said it "has had contact with the Norwegian board regarding a possible offer, without reaching an agreement."
The British company, which also owns Spanish airlines Iberia and Vueling, is now "considering its options", it said Friday as it reported a first quarter net profit of 794 million euros, up from 57 million euros a year earlier.
The price of the Norwegian Air Shuttle share plunged by 9.9 percent on the Oslo stock exchange on Friday's news, though the price was still up more than 59 percent compared to a month ago.
Speculation rose about a possible takeover of Norwegian, Europe's third-biggest low-cost company behind Ryanair and EasyJet, after IAG announced on April 12th that it had acquired the 4.61 percent stake.
On April 26th, Norwegian said it had received "several inquiries" on the heels of IAG's flirt, but refused to disclose the courters' identities.
Norwegian is one of the few low-cost airlines to have ventured into long-haul flights, which has long been the preserve of major carriers, and has been rapidly adding routes.
But it is also heavily indebted and recently ran into financial turbulence in its bid to rapidly expand.
In March, it raised 1.3 billion Norwegian kroner (135 million euros) in a private placement of shares in order to ease financial pressure.
Norwegian has ordered dozens of the latest fuel-efficient aircraft from Airbus and Boeing as part of its plans to expand in coming years and gain a cost edge against rivals.
It is planning to divest up to 140 aircraft by putting the newest ones into a leasing structure, which would free up cash, and sell some older ones once it receives newer models.
In the first quarter, Norwegian significantly cut its net loss to 46 million kroner against nearly 1.5 billion a year before, thanks to an exceptional capital gain.
The operating loss, however, rose to 2.2 billion against 1.7 billion in the first three months of 2017, while revenue climbed 33 percent to nearly 7 billion kroner.