MONTE CARLO, Monaco—Canopius Group Ltd. announced Tuesday that it has proposed acquiring Hamilton, Bermuda-based Omega Insurance Holdings Ltd. for 83 pence ($1.32) per share.

Guernsey-based Canopius said it was seeking a “short period” in which to conduct due diligence and said that any firm offer would be conditional on the results of that exercise.

The move followed Monday's announcement that consortium Haverford (Bermuda) Ltd., lead by Mark Byrne, co-founder of Luxembourg-based Flagstone Reinsurance Holdings S.A., had made an offer to buy about 25% of Omega for up to 83 pence per share.

Canopius made an unsolicited offer for Omega, which operates syndicate 958 at Lloyd's of London, in January.

Since then, Omega said it had fielded several other approaches.

During the Rendez-Vous de Septembre reinsurance meeting in Monte Carlo, Monaco, Mr. Byrne said he had been looking for opportunities to invest in a Lloyd's of London business since stepping down from Flagstone late last year.

He said that while Omega had been hit by losses recently, including a first-half loss of $49.1 million largely because of catastrophe claims, he still considers it to be a financially strong insurer and reinsurer.

Mr. Byrne said Omega had been “scratched and dented,” but it is “not a train wreck” and he was attracted because of its focus on short-tail lines of business.

Mr. Byrne said he had decided to offer up to 83 pence per share for about 25% of the company because he was aware that at there was a significant number of shareholders resisting a sale.

Mr. Byrne’s offer takes the form of a reverse Dutch auction, whereby shareholders will be asked to tender their shares at a price of up to 83 pence per share. At the close of the offer period, Haverford (Bermuda) would set a strike price—the lowest price per share that would allow it to buy 60,240,964 Omega shares or whatever lower number of shares for which valid tenders were received.

Mr. Byrne said he would not increase his offer above 83 pence. On Sept. 9, the last day’s trading before Haverford’s offer, Omega shares closed at 66 pence ($1.05) per share.

On completion of any deal, Mr. Byrne would become a director and executive chairman of Omega, while the company’s current chairman, John Coleman, would step down.

Omega’s CEO, Richard Pexton, would remain in place, while Mr. Byrne’s father, Jack Byrne, a longtime U.S. insurance industry executive and former CEO of Washington GEICO Corp., would be expected to join the Omega board.