Dell Inc. Thursday said activist investor Carl Icahn is pushing for a huge special dividend instead of a planned $24.4 billion leveraged buyout by founder Michael Dell, and threatened the company with “years of litigation” if it doesn’t combine a vote on the deal with its annual meeting.

In a letter released by Dell Thursday, Mr. Icahn said he has a “substantial” position in the company, and asked Dell to pay a per-share dividend of $9 if the deal is voted down by shareholders. He said that by his calculations, that transaction would be superior to the current going-private offer, …