In a statement, Nasdaq said it had already received irrevocable acceptances from shareholders holding more than 35 percent of the stock.
In December, European stock market operator Euronext launched a 625-million-euro bid to acquire the Oslo Stock Exchange.
Euronext operates stock exchanges in Paris, Amsterdam, Brussels, Dublin and Lisbon.
Euronext said at the time that if the deal went through, Oslo's leading position in seafood derivatives, oil services and shipping "would further strengthen Euronext's position as the leading market infrastructure for the financing of the real economy in Europe."
Euronext said it had received acceptances, also irrevocable, from more than 50 percent of shareholders for its offer.
But the board of directors of Oslo bourse said Wednesday it considered the Nasdaq offer "the best alternative for all stakeholders... and therefore unanimously recommends that the shareholders of Oslo Bors VPS accept the offer and do not accept the offer to acquire the shares of Oslo Bors VPS made by Euronext."
"The (Nasdaq) offer is so much better, both for Norway's capital market and for our companies ... that it received the unanimous support of our board and management," the head of the Oslo exchange, Bente Landsnes, told reporters.
Nasdaq already controls all of the other stock exchanges in the Nordic and Baltic region.
Unless either Euronext or Nasdaq withdraws its bid, the future ownership of the Oslo bourse will be decided by Norwegian authorities, whose approval is required for any acquisition of more than 10 percent.
Norway's finance ministry and regulatory authorities refused to comment in detail Wednesday on the rival offers.
But Oslo bourse officials were confident they would follow the exchange's recommendation.
"There is a strategic and administrative logic in the Nasdaq offer, compared to Euronext," said the board chairwoman of the Oslo exchange, Catharina Hellerud.