Icahn owns about 5 percent of Yahoo shares and has aligned himself with Microsoft to speed a sale of Yahoo to the software company. Meanwhile Time Warner has stepped up separate talks with Yahoo and Microsoft over selling its AOL business.
Yahoo mocks the alliance between Icahn and Microsoft as an "odd-couple collaboration" which it says "continues to make misleading statements about their plans for Yahoo. It dismisses Icahn as "a well-known corporate agitator."
"Your board of directors believes strongly that the Icahn-Microsoft agenda -- as presented to us jointly last week -- will destroy stockholder value at Yahoo, serving only their very narrow special interests, clearly not your interests," Yahoo said.
Yahoo highlighted some steps designed to boost its share price. The company publicly acknowledged that it was seeking ways to "unlock the value of our Asian assets" -- holdings primarily in Japan and China worth around $9 of Yahoo's $22.77 share price.
The Sunnyvale, California-based company is also planning to rely on rival Google to sell a portion of the advertising that runs alongside its own Web search results.
While Microsoft has sought to convince Yahoo to sell its search business to Microsoft, Yahoo reiterated its strategy was to keep search and be a leading player in the two major strands of online advertising: search and display.
The company said Microsoft and Icahn's latest proposal to buy its search advertising business represented "somewhat of an improvement" but was still not a good offer.
"The Icahn/Microsoft proposal was more 'smoke and mirrors' than objective reality," the letter said.
It amplifies concerns among investors that Icahn's failure to articulate clear alternatives other than selling the company to Microsoft may limit his ability to negotiate a fairly valued deal. And it mocks Icahn's knowledge of the Internet.
Yahoo repeated earlier statements that it was still open to selling the entire company to Microsoft for $33 per share.