NEW YORK (Reuters) - Yahoo Inc on Thursday warned its shareholders that billionaire Carl Icahn's agenda presents a "significant risk" to their investment, and reiterated that it would only sell itself to Microsoft under the right terms.

The public letter posted on its website on Thursday is Yahoo Chairman Roy Bostock and Chief Executive Jerry Yang's latest appeal to shareholders ahead of its annual meeting on August 1 to fend off an attack from activist investor Icahn.

Icahn owns about 5 percent of Yahoo shares and has aligned himself with Microsoft to speed a sale to the software company. Meanwhile Time Warner has stepped up separate talks with Yahoo and Microsoft over selling its AOL Internet division.

In the letter, Yahoo said the alliance between Icahn and Microsoft "continues to make misleading statements about their plans for Yahoo.

"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 added that it is "preparing to implement (its) recently signed commercial agreement with Google that will increase cash flow."

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.

Yahoo repeated earlier statements that it was still open to selling the entire company to Microsoft for $33 per share.

(Reporting by Franklin Paul and Kenneth Li; Editing by Derek Caney)

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