Microsoft has offered to buy struggling internet firm Yahoo for $44.6 billion (€30 billion) 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 compete better.

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 e-mail, shopping and news, as well as one of the most recognised brands among online users.

Yahoo said it was examining the 'unsolicited proposal' and added  that its board 'will evaluate this proposal carefully and promptly'.

Microsoft said a combination of the companies would lead to cost savings of $1 billion a year.

Microsoft's offer of $31 per share is more than 60% above Yahoo's closing price on Thursday.

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 revitalise the company.

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 receive cash or shares in Microsoft.

Yahoo's net profit for 2007 was $660m compared with $751m in 2006. Microsoft and Yahoo had been reported in May to be exploring a  merger or alliance.