Ballmer acknowledged these negotiations in the letter and questioned why the company was not speaking to 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," he wrote.
"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 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," he said.
Ballmer said that Microsoft was growing impatient more than two months after the Washington-based software company made its unsolicited takeover offer for Yahoo. At the time, the bid represented a 62 per cent premium to Yahoo's share price.
"Steve Ballmer is an emotional guy and the emotion comes through and it's frustration," Kim Caughey, senior analyst at Fort Pitt Capital Group, a Microsoft shareholder, said.
"I really don't think it's going higher than $31. That ship has sailed."
Brendan Barnicle, who follows Microsoft for Pacific Crest Securities, told the Reuters news agency that by removing the hope of a higher bid, Microsoft had given Yahoo directors the legal cover to accept Microsoft's existing offer and fend off shareholder lawsuits.
"It's part of a highly choreographed dance and parallels the take-it-or-leave-it bidding strategy Oracle Corp has used to win a string of deals to consolidate the software industry," he said.
"The big overhang on Microsoft stock has been that they would have to raise their bid."