The letter signed by Microsoft CEO Steve Ballmer said Microsoft will take its case directly to Yahoo shareholders and work to elect a new slate of directors, if the board doesn't respond by the deadline by April 26.
The bid to buy Yahoo was made in January and announced Feb. 1.
At the time, Microsoft offered $44.6 billion, or 62 percent above Yahoo's market value. The deal is currently valued at about $41 billion, based on Friday's closing share prices.
Yahoo's board formally rejected Microsoft Corp.'s bid, saying it undervalues the company.
The Silicon Valley company has since explored alliances with Google Inc., News Corp.'s MySpace.com and Time Warner Inc.'s AOL, but no alternative to Microsoft's offer has surfaced.
Ballmer acknowledged these alternative negotiations in the letter and questioned why the company is not negotiating with Microsoft.
"This is despite the fact that our proposal is the only alternative put forward that offers your shareholders full and fair value for their shares," Ballmer wrote in the letter. "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 said the Microsoft offer has grown stronger as the time has passed.
"We believe that the majority of your shareholders share this assessment," he wrote.
Yahoo and Microsoft both lost less than 1 percent of their share of U.S. Web searches in February, the most recent month for which data are available, according to the research group comScore. During that month, Yahoo grabbed 21.6 percent of searches, more than Microsoft's 9.6 percent. Google Inc.'s share rose less than 1 point to 59.2 percent.
In the intervening weeks, Yahoo released internal projects drawn up in December that call for the company's revenue to rise more than 70 percent during the next three years.
The Web company also postponed its annual shareholder meeting, and thus the deadline for Microsoft to nominate its own slate of directors to fill Yahoo's board. A new date has not been set.