(Reuters) — Health insurer Anthem Inc. said on Saturday it had offered $46 billion in cash and stock for smaller rival Cigna Corp. but that a deal was being held up in part over what role Cigna CEO David Cordani would have in a merged company.

Anthem, the second largest health insurer in the United States, said that it had made four offers for Cigna in June, sweetening each one with a bigger total offer or an increased cash component for a premium of 35.4 percent.

The statement included a letter to Cigna's board in which Anthem said it had offered $184 per share in response to Cigna's requests, but that it could not guarantee that the CEO role would eventually go to Mr. Cordani.

Cigna spokesman Jon Sandberg declined to comment.

The announcement comes at a time when the nation's biggest insurers are positioning for deals that can give them scale in providing health plans for the elderly and disabled as well as Medicaid for the poor and large employer-based insurance, which Cigna focuses on. Insurers say being bigger will enable them to negotiate better prices with doctors.

Another insurer rival, Humana Inc., had also considering selling itself, a source familiar with the matter said in late May. The Wall Street journal last month reported that Anthem and Cigna were cited as possible buyers for that company but the companies declined to comment on the report.

Last week, the Wall Street Journal also reported that Cigna had turned down Anthem after two offers and that UnitedHealth Group Inc. was interested in buying Aetna Inc.

Aetna itself has for years been speculated on as a buyer for Cigna, but Wall Street analysts have said one barrier to such a deal would be finding a role for the chief executive of each company.

Anthem CEO Joseph Swedish wrote in a letter to Cigna's board that Mr. Cordani could be president and chief operating officer of the new company during a two-year period while Mr. Swedish remained CEO. After that time, Mr. Swedish said he would step down and that the board could appoint a new CEO.

“We were stunned that the Cigna board continues to insist on a guaranteed CEO position for Mr. Cordani over choosing to allow its stockholders to realize the significant premium being offered,” Mr. Swedish wrote.

Cigna shares closed on Friday at $155.26, down $1.15 or 0.7 percent.