The sweetened offer, which Michael Dell and his private equity backer Silver Lake publicly called their best and final proposal, is the latest twist in a seven-month long saga over the fate of Dell, whose profits are under pressure from the rise of smart phones and tablet computers.

The new bid came hours before a rescheduled vote on the buyout proposal, which has drawn strong opposition from major investors including billionaire Carl Icahn and Southeastern Asset Management.

The shareholder meeting on the deal is now set for Aug 2.

Dell's $13.75 per share bid, up from $13.65 per share previously, hinges on the computer maker's special board committee changing the rules of the voting such that the buyout will pass if the majority of votes cast by shareholders is in favour of it.

As currently written, the voting rules state a share not cast in an election counts as a "no" vote, which has proven to be tough to overcome.

The committee is seeking at least $14 per share from the buyout group in order to consider a potential change in the voting terms, a person familiar with the matter said. The committee might not endorse the proposed change even if Michael Dell agreed to bump to $14 or more, the person added, declining to be named because of the confidential subject matter.

Silver Lake, however, which is backing Michael Dell's now roughly $24.6 billion bid for Dell, would not support an increase to $14 per share, said another person familiar with the matter.

Dell shares were down 0.3 percent to trade at around $12.83 in afternoon trading on Wednesday.

"According to our latest tally, approximately 27 percent of the unaffiliated shares have not yet been voted. The presumption that these shares should be treated as if they had voted against the transaction is patently unfair," Michael Dell and Silver Lake said.

"The will of the majority of the unaffiliated shares voting on the transaction should not be thwarted by an unfair standard that counts unaffiliated shares not voting as "no" votes."

The votes that have come in so far are split evenly between yes and no, according to people familiar with the matter. That means those who abstain from voting can determine the outcome.

The buyout group believes it can get the votes to pass the deal if Dell will count just the shares that have been voted. The provision of counting non-votes as a "no" was accepted reluctantly by the bidders as it sets a very high threshold to meet, according to one of the sources.

While the new offer from the group expires at 6 p.m. EDT (2200 GMT) on Wednesday, it is likely to be extended if needed.

Icahn, who has amassed an 8.7 percent stake in Dell, is leading a charge with Southeastern against the buyout with an offer of his own. On Wednesday, he tweeted "all would be swell at Dell if Michael and the board bid farewell", and promised a statement later in the day.

Icahn and others have said Michael Dell's deal undervalues the company.

INVESTORS OUTRAGED

The new offer, with its proposed change in voting rules, did not come as good news for some.

Richard Pzena, founder and co-chief investment officer of Pzena Investment Management, which owned 0.73 percent of Dell's outstanding shares at the end of March, called the proposed change in shareholder voting rule "outrageous".

"Certainly the 10 cents wouldn't sway anybody so they have to change the rules, and if the special committee goes along with this, it would be a travesty," Pzena said.

Another investor said the new offer is not really a bump.

"This is not about how to win the deal, this is about how Michael Dell exits the process," said the Dell investor, who requested anonymity. "They're really putting the screws on the special committee but I don't see how the special committee can accept the conditions."

"That's huge," said Larry Hamermesh, a corporate law professor at Widener University School of Law in Wilmington, Delaware, of the rule change proposed by Michael Dell.

"Adding the qualifier means shares that don't show don't count where previously they did."

(Additional reporting by Jessica Toonkel, Supantha Mukherjee, Nadia Damouni and Tom Hals; Editing by Rodney Joyce, Sofina Mirza-Reid and Leslie Gevirtz)

By Poornima Gupta, Soyoung Kim and Greg Roumeliotis