To that end, Icahn raised the acrimony by telling shareholders in a separate, open letter Monday that the struggling PC maker has a major liability that can easily be removed to improve company value.
"If Dell can replace Michael Dell, I think that the company would be worth far, far more," Icahn wrote.
A Dell spokesman declined to comment on Icahn's letters.
Last week, a group led by Michael Dell and the investment firm Silver Lake Partners raised its buyout offer for the Round Rock, Texas, company to $13.75 per share, up a dime from $13.65.
But they also want a change in the voting rules. They say the offer's fate must be decided by the shareholders who choose to vote either in favor of the plan or against it.
Under the existing rules, non-voting shareholders are counted as opponents of the proposal.
Icahn and Southeastern said in their letter to the board that they believe many Dell stockholders who oppose the deal may have not voted because they knew their inaction would count as a vote against the merger. They say the group led by Michael Dell is now essentially offering to pay a dime per share for a new voting method that prevents those stockholders from rejecting the deal.
"We trust that you will see this for what it is and recognize that proper protections for stockholders of Dell should not be offered for sale to anyone at any price," the letter stated, adding that the standard for approval that counts non-voting shares is perhaps the only safeguard for shareholders included in the deal.
Michael Dell and Silver Lake have said they believe the change is "fair and reasonable" to the company's other shareholders, especially given the new offer's additional 10 cents per share for the stakeholders.
Dell and Silver Lake said last week that their new offer represents their "best and final proposal." It increases the total amount they are willing to pay shareholders by about $150 million, raising the value of the proposed deal to about $24.6 billion.
The vote on the offer has been delayed a couple times and is now scheduled for Friday.
Icahn and Southeastern contend that Dell's offer undervalues the company. They have offered a more complicated alternative, but they first need to block Michael Dell's deal and then replace the company's board in a follow-up battle.
Icahn promised shareholders he will identify a "first class person" to run the company, if he can replace the board.
"I believe you will be happier and richer if you join me in voting against the Michael Dell/Silver Lake deal," Icahn wrote.
Michael Dell first offered to buy out his company earlier this year.
He says that he can turn around Dell by spending heavily to build better tablets, while also diversifying into more profitable areas of technology, such as business software, data storage and consulting. Those changes likely will be tumultuous and temporarily lower Dell's earnings, an upheaval that Michael Dell contends will be more tolerable if the company no longer has to answer to other shareholders.
Dell shares fell 8 cents to close Monday trading at $12.86. The stock is up 27 percent since the start of the year.
Dispute at a glance
DELL DISPUTE • Investor Carl Icahn is warning that a recent offer from Dell's founder to buy the struggling computer maker bypasses an important shareholder safeguard.
THE DETAILS • Last week, a group led by Michael Dell raised its buyout offer for the company and said they also want to change voting rules on it. They say the offer's fate must be decided by shareholders who choose to vote either for or against the proposal. Previously, non-voting shareholders were counted as opponents.
BACKGROUND • Icahn and another major Dell investor, Southeastern Asset Management, oppose Michael Dell's bid and have pitched an alternative offer.