REDMOND, Washington -- Microsoft said Friday it had offered to buy struggling Internet firm Yahoo for $44.6 billion (30.0 billion euros) in a bid to take on Google in the crucial battle for online revenues.

Microsoft said the booming online advertising market "is increasingly dominated by one player" -- a reference to Google -- and suggested that with Yahoo under its wing it could better compete in the bonanza.

Online advertising sales will double from $40 billion in 2007 "to nearly $80 billion in 2010," it forecast.

Yahoo would offer Microsoft a search engine to compete with Google, a popular web portal for email, shopping and news, as well as one of the most recognized brands among online users.

Microsoft said a combination of the companies would lead to cost savings of $1.0 billion per year.

In a letter to Yahoo's directors, dated Thursday and released with its statement, Microsoft revealed that Yahoo, based in Sunnyvale, California, had rebuffed earlier acquisition overtures in February of 2007.

Microsoft said it had proposed $31 per share to Yahoo's board, "representing a total equity value of approximately $44.6 billion," the statement said.

The offer represents a 62 percent premium above the closing price of Yahoo stock on Thursday, it said.

"We have great respect for Yahoo, and together we can offer an increasingly exciting set of solutions for consumers, publishers and advertisers while becoming better positioned to compete in the online services market," said Microsoft's chief executive officer Steve Ballmer.

The announcement came a day after Yahoo chief executive Terry Semel left the Internet firm's board of directors.

Yahoo had announced plans two days earlier to lay off 1,000 employees as part of an effort to revitalize a company that analysts say strayed from its profitable strengths while Semel was at the helm.

Yahoo has been hit by sluggish revenue growth despite launching a new online advertising platform a year ago and having hundreds of millions of users worldwide.

Under the Microsoft offer, Yahoo shareholders can elect to receive cash or a fixed number of shares of Microsoft stock, with its total offer consisting of one-half cash and one-half stock.

Microsoft said it believed the proposed combination would get a stamp of approval from regulators and be completed in the second half of 2008.

"We believe our combination will deliver superior value to our respective shareholders and better choice and innovation to our customers and industry partners," Balmer said.

"The combined assets and strong services focus of these two companies will enable us to achieve scale economics while reaching R and D (research and development) critical mass," said Kevin Johnson, president of platforms and services at Microsoft.

"The industry will be well served by having more than one strong player, offering more value and real choice to advertisers, publishers and consumers."

Yahoo reported that its profits dipped to $206 million in the final three months of 2007 but still topped expectations of Wall Street analysts.

Yahoo reported its revenues for 2007 climbed eight percent to $1.8 billion compared with revenues in the prior year.

However, Yahoo's net profit for 2007 was $660 million compared with $751 million in 2006.

Microsoft and Yahoo had been reported in May to be exploring a merger or alliance to better compete against Google, but no deal materialized.