HAMILTON, Bermuda—Another suitor for IPC Holdings Ltd. emerged Wednesday as Flagstone Reinsurance Holdings Ltd. made an offer for its Bermuda rival.

In a statement, Bermuda-based Flagstone said it would exchange 2.638 new common shares for each IPC common share plus $5.50 per share in cash, for a total value of $33.62 per share. IPC’s shares closed Wednesday at $27.77.

“Our offer contains a materially greater cash component and offers a greater overall value to IPC shareholders. Our offer is not subject to financing and is made on a friendly basis, with a plan to work with the existing board and management of IPC to preserve the business and franchise value of IPC in the combined entity,” Flagstone Chairman Mark Byrne said in the statement.

“We believe this approach together with the significant opportunities brought to the combined entity via Flagstone’s global underwriting platform and industry-leading technical infrastructure will maximize value for both IPC and Flagstone shareholders. We have substantially completed our confirmatory due diligence with no issues identified to date,” Mr. Byrne said.

IPC shareholders last month rejected a merger deal with rival reinsurer Max Capital Group Ltd.

Validus Holdings Ltd. made a competing offer for IPC in March and has raised its bid twice. It previously said it believes its current offer, which includes a $3.75-per-share cash component, is “full and fair” and that it would not revise the price again.