SAN FRANCISCO — Health insurer Cigna has rejected a $47 billion offer to be acquired by its larger rival, Anthem, 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, Conn.-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.