SAN FRANCISCO >> Health insurer Cigna Corp. has rejected a $47 billion offer to be acquired by its larger rival, Anthem Inc., saying the terms of the bid are inadequate and “woefully skewed in favor of Anthem shareholders.”

Cigna’s sharply worded rejection came just one day after Anthem went public with its cash-and-stock offer, which amounts to about $184 for each Cigna share or about an 18 percent premium on Cigna’s closing stock price on Friday.

The proposed deal would make Anthem an even bigger giant in an industry that many see as ripe for consolidation, as insurers struggle to cut costs in the face of new regulations and technological advances. Anthem has said the combined companies would have annual revenue of more than $115 billion and provide insurance for about 53 million people.

It’s unclear if the talks are dead. Cigna said Sunday that a deal with Anthem — “under the right circumstances” — would provide substantial benefits to consumers, doctors and investors in both companies. But in a letter signed by two top Cigna officials, the Bloomfield, Connecticut-based company added that it was deeply disappointed with Anthem’s latest offer and cited a number of obstacles to an agreement.

Among them are Anthem’s failure to address questions about possible regulatory hurdles and the massive breach of Anthem customer data that was revealed earlier this year, according to the letter signed by David Cordani, Cigna’s CEO, and Isaiah Harris Jr., the chairman of Cigna’s board.

Cigna also complained in the letter about “Anthem’s lack of a growth strategy,” while boasting that Cigna’s stock has outperformed that of its larger rival in recent years.

A spokeswoman for Indianapolis-based Anthem declined comment Sunday.

Anthem has been in talks with Cigna since last summer. It went public with its latest proposal on Saturday after four earlier bids were rejected. Anthem said one prior sticking point has been the role that Cordani would play in the combined companies.

Cigna objected Sunday that Anthem wants its CEO, Joseph Swedish, to assume outsized responsibilities as president, CEO, chairman and “head of integration” for the combined companies — which Cigna’s letter called “disconcerting and risky.”

“Nothing of this size and scale has been attempted in our sector,” the Cigna officials said of the merger.

Anthem said the total value of its proposal is nearly $54 billion, including debt.

Maneuvering between the two companies comes at a time when several other insurance companies are also reportedly engaged in acquisition talks, although they have not publicly confirmed those efforts.