Endurance Specialty Holdings Ltd. promised it wouldn’t give up on a merger with Aspen Insurance Holdings Ltd., and so it is trying again with a higher bid.

The Bermuda specialty insurance and reinsurance company disclosed on June 2 that it is now offering $49.50 per share in cash and common shares for its rival, up $2 from its initial $47.50 per share offer first disclosed in April, in a deal worth more than $3 billion.

Endurance said it is actively seeking Aspen shareholder support to boost Aspen’s board from 12 to 19 people, and would consider submitting an alternative slate of directors for vote at Aspen’s 2015 annual shareholder meeting (most would be up for re-election). Additionally, Endurance wants Aspen shareholder support for something known as a Scheme of Arrangement, which would allow a court-ordered meeting of Aspen shareholders to vote on Endurance’s proposed acquisition.

Endurance is also promoting the fact that its latest offer involves “a simplified and improved financing plan.” The latest offer includes a $1 billion bridge loan facility from Morgan Stanley.

Both companies are from the “Class of 2001” Bermuda specialty insurance and reinsurance companies formed in the wake of the World Trade Center attacks. Their merger would create a giant that handles more than $5 billion of combined annual gross premiums written. But Aspen has rebuffed Endurance’s initial overtures, claiming the buyout would lead to a loss of business. Endurance, in turn, has touted the plan as something that would boost shareholder value and create a stronger organization moving forward.

In a recent conference call with analysts, Endurance Chairman and CEO John Charman said he still wanted to pursue Aspen and “complete this transaction on a friendly basis.” He also argued that individual Aspen shareholders supported Endurance’s bid.

Endurance said it submitted its higher offer to Aspen’s board of directors on May 7 and still tried to keep things friendly, but that the Aspen board communicated less than a week later that “it was not interested in negotiating with Endurance.”

Charman, in a statement, said that Endurance “will not be deterred by an entrenched [Aspen] board and management that refuse to engage productively on the merits of our compelling proposal.” He said that Endurance would keep pushing for an M&A deal using “these and other available means to reach a successful outcome.”