The move came just hours before Dell's shareholders were scheduled to vote on the previous offer from Michael Dell and the investment firm Silver Lake Partners.
The Round Rock, Texas, company said it was delaying its shareholder meeting for a second time, moving it to Aug. 2 to give its board time to consider the offer. The meeting had been set for later Wednesday, after being delayed the week before in a sign that the offer didn't have enough shareholder support.
Michael Dell and Silver Lake said Wednesday that the new offer increases the total amount paid to shareholders by about $150 million to more than $24 billion. They say it's their best and final offer.
As part of the new offer, the group also wants to change the conditions for approval to require that a majority of the shares voted, excluding Michael Dell's stake, be in favor of the proposal. Under the current terms, the group needs a majority of all the company's outstanding shares, whether they are voted or not, excluding Michael Dell's stake, to vote in favor of it.
Dell shares slipped 5 cents to $12.83 in morning trading despite the higher offer.
In their letter to dell shareholders, Michael Dell and Silver Lake 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.
"There is simply no rational basis for shares that are not voted to count as votes against the merger agreement," the group wrote in their letter.
Two major Dell Inc. shareholders, billionaire Carl Icahn and investment firm Southeastern Asset Management, have been spearheading an effort to defeat the deal. They depict the proposal as an attempt by Michael Dell to seize control of the company at a sharp discount to its long-term value.
Icahn and Southeastern have offered a more complicated alternative, but they first need to block the deal with Michael Dell and then replace the company's board in a follow-up battle.
A spokesman for Icahn didn't immediately return an email seeking comment.
In a letter on Tuesday, Icahn and Southeastern ridiculed the four-member special committee for its stalling tactics. "Do not move election day again," they wrote. "This is not a banana republic."
Michael Dell believes he can turn around the company by spending heavily to build better tablets while also diversifying into more profitable areas of technology, such as business software, data storage and consulting. But making those changes are likely to 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's board says it want to sell to Michael Dell because it believes waiting for an uncertain turnaround is too risky. If the current deal unravels, analysts believe Dell's stock could plunge below $9, reverting back to its levels of late last year.