(Reuters) — Reinsurers Axis Capital Holdings Ltd. and PartnerRe Ltd. are considering tweaking their $6.2 billion merger agreement in a bid to fend off a $6.8 billion offer for PartnerRe by Exor S.p.A., people familiar with the matter said.

The move would be a response to Exor's announcement on Tuesday that it would sweeten its proposal, including offering 1 additional percentage point in the dividend rate received by PartnerRe preferred shareholders.

• PHOTO GALLERY: MERGER MANIA

Axis and PartnerRe are in talks about a similar plan, the people familiar with their thinking said. PartnerRe's preferred shares are worth just over $800 million, meaning the 1% bump amounts to just $8 million per year.

This relatively small amount of money could still make a difference, however, because PartnerRe's preferred shareholders control about 40% of PartnerRe's vote, making them an important constituency to win over.

In its announcement on Tuesday, Exor also said that if PartnerRe was no longer obliged to pay a $315 million fee to terminate its merger agreement with Axis, Exor would still pay out a corresponding amount to PartnerRe shareholders, effectively increasing the value of its offer to $143.89 per share from $137.50.

PartnerRe would be excused from paying the termination fee if both Axis and PartnerRe shareholders voted against the merger. Both Axis and PartnerRe see this as an unlikely scenario, and therefore do not believe there is a need to respond to that concession from Exor, the people said.

The boards of the two companies have yet to meet to consider the new plan, and its details have yet to be determined, the people added.

Representatives of PartnerRe and Axis declined to comment.

Axis' response to Exor's new terms could land in time to influence an influential report expected shortly from proxy advisory firm Institutional Shareholder Services Inc.

While Exor's cash offer would give more money to PartnerRe shareholders upfront, Axis and PartnerRe have argued that their all-share deal makes more sense over the long term given that the reinsurance industry is at a relatively low point.

Reinsurers, which help insurers pay large damage claims in exchange for part of the profit, are under pressure to consolidate after being squeezed by price competition and weak demand from insurers amid record low interest rates.

Exor has said repeatedly that it would not launch a tender offer for the PartnerRe shares.