Microsoft has set a deadline for the Yahoo board to approve its acquisition offer.

Chief executive Steve Ballmer has written to Yahoo's board of directors, imploring them to accept the offer within three weeks.

If the board does not approve the acquisition, Microsoft has vowed to appeal directly to the shareholders to replace the board with one that will green-light the deal.

"It is unfortunate that, by choosing not to enter into substantive negotiations with us, you have failed to give due consideration to a transaction that has tremendous benefits for Yahoo's shareholders and employees," wrote Ballmer.

"We think it is critically important not to let this window of opportunity pass."

The letter is the latest turn in a takeover saga now entering its third month. Microsoft made the stock offer in early February, valuing Yahoo at $44bn.

Yahoo's board rejected the offer several days later, claiming that $44bn "substantially undervalued " the company.

Microsoft has since refused to renegotiate with Yahoo, maintaining that its offer is fair and that Yahoo's shareholders mostly agree.

"The substantial premium reflected in our initial proposal anticipated a friendly transaction with you," wrote Ballmer.

"If we are forced to take an offer directly to your shareholders, 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."