(Reuters) - Italian holding company Exor (>> EXOR SpA) sweetened its all-cash offer for Bermuda-based reinsurer PartnerRe (>> Partnerre Ltd) to $6.8 billion after its previous attempt to trump a bid by Axis Capital Holdings (>> Axis Capital Holdings Limited) was rejected.

Exor, the investment vehicle of the Agnelli family, said in a statement on Tuesday it had raised its all-cash offer by 5.8 percent to $137.5 per share. PartnerRe rejected Exor's earlier $6.4 billion offer last week, arguing it undervalued the company.

Axis and PartnerRe agreed in January to create one of the world's largest reinsurers and sweetened the deal last week by including a one-off cash dividend.

Exor, PartnerRe's largest shareholder with a 9.32 percent stake, repeated that it considered its proposal superior.

"Unlike Axis, we have no intention of materially changing PartnerRe's business operations, corporate structure or

key management and employees," Exor boss John Elkann, a scion of the Agnelli family, said in his offer letter.

An Exor spokesman said the new bid would be its final one.

One of PartnerRe's top-five shareholders told Reuters that Exor's sweetened offer was "clearly superior" to the Axis deal, reflected in the Bermuda-based insurer's share price on Tuesday.

Franklin Mutual Advisers LLC said the Axis deal would "be voted down, no question about it".

PartnerRe shares were up 1.7 percent at $135.14.

PartnerRe and Axis declined to comment.

Exor, which also controls carmaker Fiat Chrysler Automobiles , has been keen to branch out into the financial services sector with its steadier and higher returns.

PartnerRe said last week it was not a good time to sell due to insurers' low valuations.

Reinsurers, who help insurers pay large damage claims in exchange for part of the profit, are being squeezed by price competition and weak demand from insurers.

People familiar with Axis' thinking said they thought Exor was offering to pay for PartnerRe at book value, below the valuations typical for deals in the reinsurance industry, adding the merger of equals between Axis and PartnerRe promised a stronger combined entity in the longer term.

However, Axis "may be limited in its ability to sweeten its offer," Clifford Gallant, an analyst at Nomura, said in a note.

"Led by Exor, PartnerRe's largest owner, shareholders may attempt to force the board to accept the bird in the hand."

Exor said it had filed material with U.S. market regulator SEC to allow it to solicit PartnerRe investors to vote against the Axis transaction should its own offer be spurned again.

Shares in Exor closed down 1.8 percent at 41.6 euros, compared with a 0.9 percent fall in Milan's blue-chip index <.FTMIB>.

(Writing by Agnieszka Flak in Milan, additional reporting by Avik Das in Bengaluru and Stephen Jewkes in Milan; Editing by Janet Lawrence and Susan Thomas)

By Mike Stone and Richa Naidu

Stocks treated in this article : Axis Capital Holdings Limited, Partnerre Ltd, EXOR SpA