Endurance Specialty Holdings Ltd. – bound and determined to acquire Aspen Insurance Holdings Ltd. – launched an exchange offer for all outstanding shares of its Bermuda reinsurance rival, dogged even after the rejection of two M&A overtures since April.

Even so, Aspen said in a prepared statement that it will give the review offer consideration “consistent with its fiduciary duties.” Still, Aspen emphasized in its prepared remarks that it will continue to emphasize with its shareholders the benefits it sees in remaining independent.

“As demonstrated by Aspen’s strong first quarter results, the company is delivering on a strategic plan to generate strong growth and shareholder value,” Aspen said in its response to the Endurance deal announcement. But “the board of directors of Aspen will carefully review the exchange offer in consultation with its independent financial and legal advisors and determine the course of action that it believes is in the best interests of Aspen and its shareholders.”

Aspen urged its shareholders to take no action until the board the board gives them its recommendation regarding the exchange offer. That’s expected within ten business days, and Aspen will file those remarks as a formal statement with the U.S. Securities and Exchange Commission.

Endurance said earlier in June that it would keep trying to acquire Aspen in a multi-pronged plan that included a push to expand Aspen’s board, and a quest to gain shareholder support for a vote on a Scheme of Arrangement, which would let Endurance acquire all of Aspen’s outstanding shares despite the board’s previous resistance.

Endurance announced June 9 that it had commenced its exchange offer for all of Aspen’s outstanding shares. As outlined, each person or investment firm holding Aspen common shares has the right to receive all cash ($49.50); all Endurance common shares (0.9197 Endurance shares for each Aspen share); or a combination of cash and Endurance common shares (0.5518 Endurance common shares and $19.80 in cash for each Aspen Share). Ideally, Endurance wants to snatch up Aspen with a mix of 40 percent cash and 60% Endurance common shares, based on Endurance’s closing price on April 11.

The $49.50 per share price is $2 higher than Endurance’s initial offer in April, and both offers are at a premium above Aspen’s closing price of $46.34 as of June 9 (itself about $7 higher than Aspen’s average price before Endurance’s initial April offer). Aspen’s board has rejected the offer as damaging to its own interest, and the company has question whether an M&A deal as outlined would be financially responsible.

Endurance said the exchange offer will expire Aug. 29, 2014 at 5 p.m. unless otherwise extended. Deadline or not, Endurance Chairman and CEO John Charman argued in a statement that the launch of the exchange offer shows his company is serious about an M&A deal with Aspen.

“The commencement of the exchange offer today further demonstrates our full commitment to a transaction with Aspen, and provides an additional mechanism for shareholders to support the consummation of this very compelling combination,” Charman said. “We again call on Aspen’s board and management to act in the best interests of Aspen’s shareholders by engaging with us in constructive discussions regarding our increased proposal and to case with their rhetoric and entrenchment.”

Needless to say, this is “to be continued.”