Michael Dell and Silver Lake Partners on Wednesday rejected a demand for a higher bid from Dell's special committee, saying the $13.75 per share offered is a "full and fair price" and that the amount, increased by a dime per share earlier in the morning, represents their best and final bid, sources familiar with the situation told CNBC.
Rival bidder Carl Icahn tweeted in apparent reaction: "All would be swell at Dell if Michael and the board bid farewell."
The committee was said to be seeking at least $14 per share from Michael Dell and Silver Lake in order to consider a potential change in voting rules, according to a person familiar with the matter.
The special committee might not endorse the proposed changes in voting rules even if the buyout group raised its takeover offer to $14 per share or more, the person added, asking not to be named because he was not authorized to speak with the media.
Founder Michael Dell pushed earlier Wednesday for easier voting rules to help him win his battle to take the PC maker private and offered 10 cents more per share, or $150 million, to $13.75 per share to sweeten his $24.4 billion bid.
The new proposal is for approval to be based on a majority of votes cast by unaffiliated shareholders, giving Michael Dell and Silver lake Partners, his private equity backer, a leg up in the face of opposition from billionaire investorIcahn and several other investors.
The bidders had fallen short of the previous bar to success—majority support of all unaffiliated shareholders, sources familiar with the matter said last week.
(Read more: Icahn rips intoDell board...and slams Ackman, too)
The proposed voting change would stop shareholders who abstained from voting being counted against the deal.
"That's huge," said Larry Hamermesh, a corporate law professor at Widener University School of Law in Wilmington, Del. "Adding the qualifier means shares that don't show don't count where previously they did."
"It would be unconscionable if Dell directors except this new offer," Dell shareholder Rich Pzena told CNBC Wednesday. "Any shareholder who voted for this should rethink their vote because you are setting a precedent that Directors can be complicit in management's efforts to steal companies from shareholders who don't want to sell."
Pzena added: "I urge shareholders who voted for this to switch their vote in protest."
(Read more: Carl Icahn: I've never seen a board as bad as Dell's)
Dell shares rose 1.8 percent to $13.11 in pre-market trading on Wednesday. (Click here for the lates quote on Dell.)
Dell postponed a shareholder vote for the second time to Aug. 2 and said the new proposal would be considered by its special committee of independent Dell directors.
"This is our best and final proposal," the bidders said in a letter to Dell's board.
Icahn, who has amassed an 8.7 percent stake in Dell, is leading a charge with major shareholder Southeastern Asset Management against the buyout with an offer of his own.
He and others say Michael Dell's deal undervalues the world's No. 3 personal computer maker.
Hamermesh said those who had abstained previously might have known that their holding would be counted as a "no" and they might now have an incentive to vote.
"We continue to oppose the Dell proposal." Jason Subotky, co-manager of the Yacktman Funds, told CNBC.
Dell stock closed at $12.88 on the Nasdaq on Tuesday.
-- CNBC contributed to this report.