Connecticut patients who receive medical care through Anthem Blue Cross Blue Shield could face higher costs after the insurance provider and Hartford HealthCare failed to agree on a new three-year contract.

Anthem spokeswoman Sarah Yeager said Saturday that Hartford HealthCare rejected Anthem’s offer. She says the health system wanted three years of consecutive cost-of-living increases that are “two to three times the rate of inflation” each year.

Hartford HealthCare spokesman Shawn Mawhiney says Anthem is paying other providers more than it pays HHC.

Due to the missed deadline, state patients insured through Anthem are considered out-of-network. They could pay higher out-of-pocket costs at hospitals in the system beginning Oct. 1.

Yeager says Anthem will try to transition customers now considered out-of-network to other providers and hospitals.