The health insurer Aetna said on Friday that it had agreed to acquire its smaller rival Humana for $37 billion in cash and stock, signaling the start of what may become a flurry of consolidation in the sector.

The deal would bring together two of the biggest health insurers in the United States. The combined company would have estimated operating revenue of $115 billion this year and serve more than 33 million people.

The proposed merger occurs as the nation’s largest for-profit health insurers seek ways to reduce costs and capitalize on growing opportunities in the government and individual markets. The companies say they will be able to operate more efficiently and negotiate more effectively with large health systems, which have also been consolidating.

The acquisition “will significantly advance our strategy of more effectively serving members in a rapidly changing health care industry,” Mark T. Bertolini, Aetna’s chairman and chief executive, said in a news release. Mr. Bertolini would assume the same roles in the combined company. The company’s board would be expanded to 16 members and include four Humana directors.