AP Business Writer

NEW YORK (AP) _ After getting the cold shoulder, U.S. health insurer Anthem Inc. said it’s raising its offer to buy rival Cigna Corp. for $54 billion, including debt.

Indianapolis-based Anthem said Saturday it’s proposing $184 per share, which it says represents a premium to Cigna’s stockholders of more than 35.4 percent based on the closing price of Cigna’s share on May 28.

Anthem said it has been in talks with Cigna, based in Bloomfield, Connecticut, to explore a potential combination since August 2014 and said made its proposal public because the companies have not been able to come to an agreement. The company also said it has submitted four written proposals since early June, and made previous offers of $174 per share and $178 per share, according to the letter to Cigna’s board of directors that Anthem made public Saturday.

In the statement, Anthem said that the combined company would be “an industry leader” with greater than $115 billion in annual revenue. It noted that Anthem and Cigna together “would gain meaningful diversification” covering about 53 million combined medical members and strong commercial, government, consumer and specialty franchises.

“This combination is the absolute best strategy for both organizations to maximize the potential and lead the transformation of the health care industry,” said Joseph Swedish, Anthem CEO in a statement.

Officials at Cigna couldn’t be reached immediately for comment.

The announcement comes as investors have been speculating for weeks about the possibility of a major acquisition in an area where size is becoming increasingly critical. Health insurers have also been hoarding cash from recent strong quarters and doing little to tamp down merger talks. An Anthem executive told analysts last month that he thought the industry would continue to consolidate.

The Wall Street Journal also reported in late May that the Medicare Advantage coverage provider Humana, based in Louisville, Kentucky, is considering a sale. Shares of that company soared well past $200 each to reach all-time high prices. A few days later, Humana said it was pulling out of a major health care conference, wouldn’t comment on merger rumors and would decline to comment until its second-quarter results are reported in late July.

Scale or size is critical for health insurers because it gives them more negotiating power when they hash out rates with care providers. It also allows them to spread underwriting and claims processing costs over a bigger base of customers.

Cigna’s shares closed down $1.15 per share to $155.25 Friday, while Anthem’s shares were down 18 cents to $165.06.