Federal lawmakers and state officials are stepping up pressure on insurers to allow consumers whose coverage has been canceled in response to the health overhaul to keep their policies beyond the end of the year.

On Tuesday, one of the largest regional health plans in the nation, Blue Shield of California, said it would relax its stance on terminated policies for about 115,000 people after state regulators demanded it do so. Customers now will have until March to decide which plan to choose for 2014, a three-month extension. Because the newer plans generally cost more, the extension could save residents as much as $28.6 million on premiums, said Dave Jones, California’s insurance commissioner.

“For 115,000 people, they get additional time to decide what’s best for them and their families,” he told reporters Tuesday. The California Department of Insurance is reviewing termination letters sent by other insurers in the state to decide whether other companies need to offer consumers similar extensions, Mr. Jones said.

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