During an Endurance Specialty Holdings Ltd. investor call on June 2, one thing became perfectly clear. John Charman, the company’s chairman and CEO, is miffed at the board and executive leadership of rival Aspen Insurance Holdings Ltd. and its continued outright rejection of Endurance’s M&A overtures.

During the call, Charman insisted that individual shareholder support is there, both for the initial $47.50 per share cash and stock bid to by Aspen first announced in April, and the $49.50 per share higher offer Charman said Endurance proposed to Aspen’s board early last month, before it summarily rejected the now $3.2 billion offer on May 12. The latest bid is at a 25.7 percent premium to Aspen’s unaffected closing share price of $39.37 on April 11, 2014. Endurance disclosed its second, bigger bid on June 2 and held an investor call to explain why it is now taking its case for acquisition directly to Aspen shareholders.

“We have had positive dialogue with the shareholders of both Aspen and Endurance, and they have indicated overwhelming support,” Charman said during the call. “Unfortunately, Aspen’s board and management continues to stubbornly and summarily refuse to engage with use in any manner whatsoever, even when we presented them with our increased proposal. Given we have provided them with more than ample time to engage with us, we have decided it is time to move forward and engage directly with Aspen’s shareholders, in order to give them a voice and a way forward that they have asked for and deserve.”

Aspen issued a statement later on June 2 both reiterating its rejection of Endurance’s latest offer, and explaining why it still believes shareholders will gain more in the long run if it continues on an independent path.

“In addition to grossly undervaluing Aspen, the proposal represents a strategic mismatch and, based on our conversations with major clients and brokers, would result in significantly greater dis-synergies than Endurance claims,” Glyn Jones, Aspen’s chairman of the board of directors, said in a statement. “Moreover, the revised proposal does nothing to address additional serious concerns we raised with respect to Endurance’s prior proposal, including a stock consideration that is highly unappealing and financing terms that remain unclear and lack certainty.”

Jones added that Aspen remains confident that it “can achieve more value for its shareholders – and without the risks that are inherent in a merger with Endurance – by continuing to execute its standalone plan.” Jones said Aspen’s generally successful 2014 first quarter results reflect this, and that Endurance’s strategy to pursue an acquisition at this point ignore Aspen’s value and reflects “coercive legal tactics in a desperate attempt to continue to advance an unattractive proposal that neither our board nor our shareholders support.”

In a word: Ouch.

Endurance has said it will take a multipronged approach now to win the support of Aspen Shareholders, including a $1 billion bridge loan from Morgan Stanley to help fund the cash and stock transaction.

In a more aggressive move, Endurance said it plans to seek the support of shareholders owning at least 10 percent of Aspen’s outstanding common stock (the minimum required under Bermuda law) to convene a special general meeting that would vote on boosting Aspen’s board of directors from 12 to 19 members. If approved, most of the existing board would be up for reelection at Aspen’s 2015 annual meeting and “Aspen’s shareholders would have the ability to hold the board directly accountable” by replacing most of them. Endurance may also nominate board candidates at that time, should its plan reach this point.

Additionally, Endurance would seek the support of Aspen shareholders to push for a court-ordered meeting to vote on a Scheme of Arrangement. Under Bermuda law, this would allow Endurance to acquire all of Aspen’s outstanding shares. Investors holding at least 15% of Aspen’s outstanding common shares could pursue this action under Bermuda law, without the approval of Aspen’s board.

Aspen, in its response, noted that the Scheme of Arrangement, or involuntary scheme, essentially amounts to a hostile acquisition, and said the legal maneuver has yet to work in Bermuda. Aspen also knocked Endurance’s plans to stuff Aspen’s board with supporters and then potentially nominate its own slate of directors, suggesting the maneuvers would lead to disaster.

“Aspen continues to believe that Endurance simply has no clear or compelling path to force its unattractive proposal on our board and our shareholders,” Jones said. “We intend to defend vigorously against these latest coercive tactics by Endurance.”

Endurance CFO Michael McGuire said during the call, however, that executives will file documents with the SEC to start moving this latest M&A strategy forward, with details expected to be mailed to Aspen shareholders. He added he should know how successful Endurance’s more aggressive stance ends up, by sometime in July.

Charman added he still sees the merger as making “a great deal of strategic and financial sense,” and that Endurance executives “stand ready and willing to meet with Aspen and its advisors to make this transaction a reality.”

If resistance continues, however, Charman said Endurance “will take continued steps as necessary to see this transaction through.”

In other words, both Endurance and Aspen face a dramatic summer.