SAN FRANCISCO (Reuters) - Yahoo Inc (YHOO.O) has three weeks to accept Microsoft Corp.'s (MSFT.O) $31 per share cash-and-stock offer or Microsoft will mount a proxy battle to win investor support for the takeover, Microsoft said on Saturday.

Microsoft Chief Executive Steve Ballmer said in a letter dated April 5 and addressed to Yahoo's board of directors that "now is the time" to negotiate final terms of a deal, one which would mark the biggest takeover yet in the high-tech industry.

"If we have not concluded an agreement within the next three weeks, we will be compelled to take our case directly to your shareholders, including the initiation of a proxy contest to elect an alternative slate of directors," Ballmer wrote.

A Yahoo spokeswoman was not aware of the letter and would not immediately comment on Yahoo's reaction to the move.

Ballmer said Microsoft is growing impatient more than two months after the Redmond, Washington-based software behemoth made its unsolicited takeover offer for Yahoo. At that time, the bid represented a 62 percent premium to Yahoo's share price.

"While there has been some limited interaction between management of our two companies, there has been no meaningful negotiation to conclude an agreement," Ballmer wrote.

The Microsoft letter argues that the economy and the market for Internet stocks have deteriorated in the intervening period, and that Yahoo's share of Web search and online advertising business has declined, referring to industry market reports.

"During these two months of inactivity, the Internet has continued to march on, while the public equity markets and overall economic conditions have weakened considerably," Ballmer wrote.

Meanwhile, Yahoo has adopted measures that make a merger with Microsoft more costly, Ballmer complained.

(Reporting by Eric Auchard in San Francisco and Daisuke Wakabayashi in Seattle, editing by Philip Barbara)