By Mike Stone

June 1 (Reuters) - Bermuda-based reinsurers PartnerRe Ltd and Axis Capital Holdings Ltd are embarking on a public campaign this week to convince shareholders of the merits of their $13 billion merger, with their top executives leading the charge.

Exor SpA, the investment vehicle of Italy's Agnelli family, has attempted to derail the merger of the two companies by offering $6.8 billion for PartnerRe. However, PartnerRe still maintains that Axis' offer is superior.

PartnerRe and Axis have now decided to ask their respective shareholders to vote on the deal on July 24, according to people familiar with the matter who asked not to be identified because this information has not yet been released to the public.

"Now we are moving forward because the Exor offer is unacceptable by any metric. So on that basis we have no hesitation," PartnerRe Chairman Jean-Paul Montupet said in an interview.

Exor Chief Executive John Elkann hosted a conference call on Friday and said his firm would not raise its offer, but added that it was willing to negotiate with PartnerRe if the latter's board declared Exor's bid reasonably likely to be a superior proposal to that of Axis.

Axis and PartnerRe agreed in January to merge to create one of the world's largest reinsurers, responding to intensifying pressure in the industry to consolidate.

Axis' stock offer for PartnerRe, currently worth $131.50 per share, including a special cash dividend of $11.50 per share, is below that of Exor, which is for $137.50 per share all in cash.

Nevertheless, sources close to Axis have previously said that an all-share deal makes more sense if one believes that this is a bad time in the industry's cycle to cash out.

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

Axis and PartnerRe will argue that the actual economic book value of PartnerRe is between $143 and $151 per share when PartnerRe's reserves are added to the estimated book value of the company at the end of the year, when it is expected to close.

"The merger with Axis is tremendously compelling and delivers significant value to our shareholders, as well as substantial value to brokers and customers. It is a tax-free, highly unique opportunity that allows for continuity and great upside for our investors," Montupet said.

The debate on a cash offer versus a 90 percent stock offer with a cash dividend has divided shareholders. Proxy advisory firms ISS and Glass Lewis have yet to weigh in with their recommendations on the transaction.

Exor has said that it will keep its fully financed offer on the table until after the PartnerRe shareholder vote. If PartnerRe shareholders do not vote for the Axis deal, PartnerRe's board would be free to adopt the $137.50 per share offer to make way for a friendly deal.

Exor has become PartnerRe's largest shareholder after acquiring a stake of 9.9 percent in the common equity, a move the reinsurer said was a "coercive attempt to further its opportunistic acquisition at the expense of PartnerRe's long-term shareholders".

But PartnerRe's shareholder base includes preferred shares, which comprise 40 percent of the shareholder voting base. The preferred shareholders will roll over their stakes should PartnerRe be sold.

Axis hopes PartnerRe preferred shareholders will favor its deal because they argue that Exor would borrow too much money to purchase PartnerRe, with the debt burden weighing on the value of the shares.

"We are highly confident that given the strategic benefits of our merger, expense synergies, and capital efficiencies, we will achieve a 12 percent-plus return on equity (ROE) in 2017 without making any heroic assumptions," Albert Benchimol Axis's CEO said in an interview. Most reinsurers achieve high single digit ROE.

An Exor spokesman did not respond to a request for comment.

(Reporting by Mike Stone in New York; Editing by Richard Pullin)