BOSTON/SEATTLE (Reuters) - Yahoo Inc's  second-biggest shareholder urged Microsoft Corp to raise its $42 billion bid for the Web pioneer and warned Yahoo it has few options other than to accept, raising pressure for them to seal a deal.

In a quarterly letter to investors released on Tuesday, Bill Miller, the star stock-picker at U.S. asset manager Legg Mason Inc, estimated fair value for Yahoo to be near $40 per share, versus Microsoft's original offer of $31 per share.

Microsoft "will need to enhance its offer if it wants to complete a deal," Miller wrote in a letter dated February 10, one day before Yahoo formally rejected Microsoft's proposal for the company.

"It will be hard for (Yahoo) to come up with alternatives that deliver more value than (Microsoft) will ultimately be willing to pay," wrote Miller. "We think this deal is a strategic imperative for (Microsoft) and that (Yahoo) is in a tough spot if it wishes to remain independent."

Miller is the first major institutional Yahoo shareholder to publicly comment on Microsoft's unsolicited bid.

Institutional shareholders hold about 75 percent of Yahoo's stock, according to Reuters data, versus 10 percent for company insiders, including co-founders David Filo and Jerry Yang.

Legg Mason Capital Management, the unit of Legg Mason headed by Miller, owns over 80 million shares of Yahoo, or a 6 percent stake in the company, trailing only Capital Research & Management's 11 percent holding.

Yahoo on Monday turned down Microsoft's bid, currently valued at $41.7 billion, saying it did not properly assess the value of Yahoo's wide-reaching audience, online advertising investments, cash-generating ability and growth prospects of its overseas holdings.

Microsoft responded by saying its offer was "full and fair," but stopped short of saying it would not raise its price.

Redmond, Washington-based Microsoft also said it reserved the right "to pursue all necessary steps" without specifying if it plans to take its bid straight to Yahoo shareholders.

COUNTER OFFER

Analysts expect Microsoft to raise its bid to at least $35 a share, but could be persuaded to go as high as $40.

Yahoo shares are now trading at a 2 percent premium to Microsoft's cash-and-stock deal, indicating that investors are expecting Microsoft to raise its bid.

Legg Mason's Miller noted that Yahoo shares had been trading at a four-year low prior to Microsoft's offer and the stock was trading above Microsoft's bid price for all of 2004.

Yahoo shares fell 30 cents, or 1.0 percent, to $29.57 on the Nasdaq. Microsoft shares rose 13 cents to $28.34.

Yahoo continues to lose Web search market share to Google Inc. Last month, it disappointed Wall Street with its 2008 revenue outlook as it promised to cut jobs and invest more in online advertising work.

According to employees at the Sunnyvale, California-based company, Yahoo began carrying out those lay-offs of up to 1,000 employees on Tuesday. A Yahoo spokeswoman declined to comment.

Citigroup issued a research note on Tuesday saying the most likely scenario, with a 55 percent probability, was that Microsoft will offer a higher bid to clinch a deal with Yahoo.

"Given the likely lack of alternative bidders, (Yahoo's) limited strategic options, and our view that buying (Yahoo) may be (Microsoft's) ONLY game changing option in Online Advertising, we believe this is the most likely scenario," Citigroup analysts said.

The second most probable scenario with a 30 percent chance, according to Citigroup, is that Yahoo remains independent and outsources its search to Google.

(Additional reporting by Eric Auchard in San Francisco; Editing by Andre Grenon)

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