NEW YORK (Bloomberg) — Nasdaq Stock Market Inc. put its stake in London Stock Exchange up for sale, abandoning an 18-month effort to buy the UK market and focus on the battle for control of Sweden's OMX AB.

Nasdaq, the second-biggest US equity exchange, was twice rejected in attempts to buy LSE. About $1 billion of proceeds from selling the 31 percent stake would be used to retire debt and buy back shares, Nasdaq said in a statement yesterday. The sale would increase earnings per share by as much as 35 cents next year, the company said.

The New York-based exchange gave up on purchasing the LSE three days after Borse Dubai, owner of Dubai's two stock exchanges, trumped its bid for OMX. Chief Executive Officer Robert Greifeld, who needs about $355 million to top Dubai's 27.7 billion kronor ($3.96 billion) bid, said last week that Nasdaq can afford to alter its offer.

"Nasdaq is in a difficult position, with this significant stake in the LSE worth a sizeable chunk of money that they don't have strategic control of," said Henk Potts, who helps oversee $45 billion at Barclays Stockbrokers in London. "They probably feel they could better use the financial firepower elsewhere rather than leave it sitting idle."

Exchanges worldwide are racing to strike deals to meet competition from rivals who have already announced more than $64 billion in acquisitions and joint ventures since 2005, data compiled by Bloomberg show. NYSE Group Inc.'s $14 billion purchase of Paris-based Euronext NV in April created the first trans-Atlantic stock exchange.

Nasdaq fell 23 cents to $31.52 at 4 p.m. in New York. OMX closed with a 2.2 percent gain to 237 kronor in Stockholm, while LSE rose 2.4 percent to 1,301 pence in London trading.

Nasdaq first acquired shares of LSE on March 30, 2006, and ultimately paid $1.33 billion for its stake, according to regulatory filings. As of June 30, the investment produced gains of $333 million, helped by an increase in LSE shares and the value of the British pound, an August 1 filing with the US Securities and Exchange Commission shows. JPMorgan Chase & Co. and UBS AG will manage the sale of the stake, Nasdaq said.

The sale may take a month and bids from rival exchanges will be accepted, Greifeld told analysts today in a conference call. In a separate statement, Nasdaq said it won't sell its entire stake in the LSE to a single buyer.

Nasdaq's board of directors made the decision within the past two weeks to sell the stake after investors ignored the rising value of the LSE holdings, Greifeld said.

"If you back out the LSE stake from our earnings, you see that our price-to-earnings ratio is at a ridiculously low level," he said. "Our shares are significantly undervalued and trade at a discount."

Nasdaq is the cheapest publicly traded US exchange, fetching 25 times next year's estimated earnings, according to Bloomberg data. NYSE Euronext trades for 29 times next year's profit.

Borse Dubai last week offered to pay 230 kronor a share in cash for OMX, which operates seven Nordic exchanges and provides trading systems for markets in more than 50 countries. The exchange already holds shares and options that give it control of a 28.4 percent stake in OMX.

Before the rise in Nasdaq shares today, the US exchange's bid was valued at about 205 kronor. In May, Nasdaq agreed to pay 94.3 kronor a share in cash, and issue 0.502 of its shares for each OMX share.

Greifeld is meeting this week with OMX shareholders and executives in Sweden to discuss the deal. He said Nasdaq would follow its practice of striking deals that contribute to earnings after about 18 months.

"We will maintain our M&A discipline with respect to both price and the terms of our offer," Greifeld said. "It is my goal to sit down with the OMX shareholders, talk through our bid in the current environment and determine how to best meet their needs."

OMX views the bid from Borse Dubai as hostile, newspaper Dagens Nyheter reported today, citing Chairman Urban Baeckstroem. He first learned of the approach from reports on the Internet and said it is "obvious" the Dubai stock exchange doesn't care about the opinion of the board of the Swedish exchange, according to the newspaper.

Borse Dubai CEO Per Larsson said yesterday his company's offer would enable OMX to access the developing markets of the Middle East rather than being acquired by an organization focused on the US, where growth is slower and competition is higher. Larsson said he was speaking with OMX executives "for some time" before their accord with Nasdaq prevented further talks.

"Our offer is 15 percent higher than Nasdaq," Larsson said in an interview. "It's the best offer."

Selling the LSE stake may bolster Nasdaq's share price, boosting the value of its cash-and-stock offer for OMX, said Fox- Pitt, Kelton Inc. analyst Ed Ditmire. Nasdaq may not have to surpass Dubai's bid for OMX to succeed, he said.

"The Dubai bid, which implies singular ownership of the OMX by a foreign government entity, has unusual implications, which could preclude some shareholders' support despite its nominally higher value," said Ditmire, who has an "outperform" rating on Nasdaq shares.

Nasdaq's Greifeld unsuccessfully tried to open acquisition talks with LSE in March 2006. LSE CEO Clara Furse rejected a second, higher offer November. Shareholders of the London bourse voted against Nasdaq's offer three months later.

LSE last month gained shareholder approval for the 1.63 billion-euro purchase of Borsa Italiana SpA. The takeover will reduce Nasdaq's stake in LSE to about 22 percent.