(Reuters) - Axis Capital Holdings Ltd (>> Axis Capital Holdings Limited) is not considering improving on its offer for Bermuda-based reinsurer PartnerRe Ltd (>> Partnerre Ltd) following rival bidder Exor SpA's (>> EXOR SpA) raised $6.8 billion (4.32 billion pounds) bid, a person familiar with the matter said on Sunday.

Axis' steadfastness underscores its confidence that its all-stock offer for PartnerRe, currently worth $132 per share including a special dividend of $11.5 per share, is superior to the sweetened $137.5 per share all-cash offer tabled last week by Italy's Exor, the investment vehicle of the Agnelli family.

The source asked not to be identified because Axis' deliberations are confidential. Representatives for Axis and PartnerRe declined to comment.

Unlike Exor's offer that would cash out all PartnerRe shareholders, the deal with Axis would leave PartnerRe shareholders owning 51.6 percent of the combined company, with Axis investors owning the rest.

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. Sources close to Axis have previously said that an all-share merger of equals makes more sense if one believes that this is a bad time in the industry's cycle to cash out.

PartnerRe has signed a merger agreement with Axis, but due to the back and forth between the rival bidders, it has not yet scheduled to have its shareholders vote. It has also yet to say whether it still prefers the Axis offer following Exor's raised bid on May 12.

Under the agreement between PartnerRe and Axis, PartnerRe shareholders will receive 2.18 common shares of the combined company for each PartnerRe common share they own, while Axis shareholders will receive one common share of the combined company for each common share they own.

When Exor increased its offer for PartnerRe, it also announced that it had become PartnerRe's largest shareholder with a 9.32 percent stake. If Axis' offer for Partner Re is put to the latter's shareholders for a vote, Exor will likely vote its block of shares against the transaction.

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.

(Reporting by Mike Stone in New York)

By Mike Stone

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