Health insurance company Cigna rejected a bid from Anthem Sunday, turning down a $53.8 billion offer from its larger competitor, saying the joint venture wouldn’t have the best interests of Cigna shareholders in mind.

"We are deeply disappointed with your recent actions," the company said in a letter signed by Cigna CEO David Cordani and Chairman Isaiah Harris. "We have been engaged in good faith discussions with Anthem to determine whether a potential strategic combination is in the best interests of Cigna's shareholders.”

Anthem, the largest for-profit healthcare company in the Blue Cross and Blue Shield Association, confirmed the two companies had been in serious talks since May, CNBC reported Sunday. The Indianapolis company said it was “frustrated” with Cigna’s requests, even raising its offer to $184 per share following Cigna’s rejection of three offers starting June 3. The offer represented more than a 35 percent premium to Cigna’s close on May 28, when both companies began discussions.

Anthem CEO Joseph Swedish said Cigna’s board insisted on keeping control of the combined venture, naming Cordani as chief operating officer of the new company, with Cigna maintain six seats on the 14-member board.

"Despite the compelling aspects of these proposals, you continued to insist that Mr. Cordani be immediately appointed CEO of the combined company, or that we reach an acceptable position for his specific roles and responsibilities as well as the timing for a transition to CEO," Swedish said in a letter Saturday.

Cigna also requested "that there be an almost equal board split of directors in the combined company and that certain changes related to senior leadership changes," a requirement that Anthem didn’t accept.

"You are … facing a number of major issues, including Anthem's lack of a growth strategy, complications relating to your membership in the Blue Cross Blue Shield Association and the related antitrust actions, and other significant challenges, such as the massive data breach you experienced in February," Cigna responded in a letter. "In fact, these fundamental issues, and your inability to address them in the context of a strategic combination, caused your management team, at your direction, to terminate our prior discussions earlier this year.”

Humana Inc. of Louisville, Kentucky, is reported in negotiations to be acquired by Aetna Inc. of Hartford, Connecticut.