John Elkann, chief executive of Italian investment company Exor SpA, is taking his $6.8 billion offer for reinsurer PartnerRe Ltd. to its investors, hoping to thwart the Bermuda-based company's plan to merge with rival insurer Axis Capital Holding Ltd.

Mr. Elkann, a scion of Italy's Agnelli family that controls Exor, reiterated that his $137.50 a share offer for the reinsurance company will be his best. PartnerRe already rejected it and a previous $130-a-share offer, saying it preferred to stick with Axis Capital.

"When you get that much resistance from a board, which as we have learned has entrenched interests protecting their own positions, they are not really legitimized to really defend stakeholders' interests," said Mr. Elkann in an interview. "It has to be settled by shareholders."

Mr. Elkann met individually with some of PartnerRe's largest shareholders last week and Tuesday plans a meeting at New York's St. Regis hotel to seek wider support for his improved offer. He is on the board of News Corp, which owns The Wall Street Journal.

PartnerRe shareholders will have the final say at a meeting in Bermuda on July 24 called to vote on the Axis tie-up. The outcome is uncertain, in part because the vast majority of PartnerRe's shares are dispersed among institutional investors that haven't declared how they will vote. Since making its initial offer, Exor has acquired almost 10% of PartnerRe to become the reinsurer's largest shareholder.

"The PartnerRe board has acted and continues to act in the best interests of the company and all of its stakeholders, and the merger of equals with Axis Capital is the result of a thorough exploration of strategic opportunities," PartnerRe Chairman Jean-Paul L. Montupet said in an email on Monday.

Exor's all-cash bid is the biggest deal ever attempted by the Agnelli family holding company and part of Mr. Elkann's long-term plan to diversify its holdings. Under his stewardship Exor has already swapped Europe for the U.S. as its biggest source of revenues and has begun to lessen exposure to its main asset, a 29% stake in Fiat Chrysler Automobiles NV.

PartnerRe says its all-share deal with Axis, which would give PartnerRe shareholders 51% of the new company, will lead to $200 million in overall synergies. Following the Exor advance, PartnerRe sweetened its deal promising shareholders a special $11.50 a share dividend if they vote for the Axis tie-up.

PartnerRe shares have traded well below Exor's sweetened $137.50 offer. On Monday, its stock closed up 25 cents at $131 a share.

Exor is interested in the reinsurance business because of the current attractive valuations and the long-term outlook for the industry, said Mr. Elkann. The PartnerRe bid isn't part of a plan to use the reinsurer's premiums to diversify further Exor's assets, he said.

Some industry analysts have speculated that Mr. Elkann wants to emulate Warren Buffett whose Berkshire Hathaway Inc. more than four decades ago pioneered the practice of using insurance premiums to diversify investments.

"I have great admiration for what Buffett has achieved and built," said Mr. Elkann who has attended Berkshire shareholders' meetings. "I have studied Berkshire Hathaway and appreciated time spent with Buffett, but we could set up a hedge fund if the reason we were buying PartnerRe was just so we could invest the premiums. It would be cheaper and easier."

If the PartnerRe deal falls through Exor will look closely again at the reinsurance industry to see if there are other takeover candidates, said Mr. Elkann.

"I have a long way in front of me and I think it's important to be disciplined [and not overpay for PartnerRe]," said Mr. Elkann. "We feel this is a good opportunity at these values, but we are not going to race after it. That would be really bad in terms of setting a precedent."

Write to Eric Sylvers at eric.sylvers@wsj.com

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