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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, which, valued at more than $40 billion would mark the biggest-ever takeover 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.

Then he threatened to reduce Microsoft's offer if Yahoo failed to meet the deadline: "That action will have an undesirable impact on the value of your company from our perspective which will be reflected in the terms of our proposal."

The letter marks the tightening of the noose in a classic Wall Street bear-hug merger strategy, wherein Microsoft aims to convince Yahoo directors to negotiate a friendly deal or else face a battle for their jobs at Yahoo's next annual meeting.

Yahoo's board is reviewing the letter, said a person close to the company. Directors of the Sunnyvale, California-based company have rebuffed Microsoft's original offer, saying the bid undervalues Yahoo and that it is seeking alternatives.

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

"Steve Ballmer is an emotional guy and the emotion comes through and it's frustration," said Kim Caughey, senior analyst at Fort Pitt Capital Group, a Microsoft shareholder. "I really don't think it's going higher than $31. That ship has sailed."