Health insurer Anthem Inc. pressed ahead with its pursuit of a $54-billion merger with Cigna Corp. despite a spurned bid and increasing concerns about industry consolidation.

Joseph Swedish, Anthem's chief executive, went on the offensive Monday trying to rally support for his takeover offer among Cigna shareholders and put pressure on the company's board, which rejected his $184-a-share offer over the weekend.

He also took on critics of health insurance consolidation who fear it will lead to higher premiums and less choice. Swedish touted the idea of a combined company that would squeeze unnecessary costs out of the healthcare system and invest in better technology and service for customers.