The policies had been set to expire on Dec. 31 but will be extended until Feb. 28 for those who choose to re-enroll. Notices informing customers of the extension will be sent out this week, Anthem said.
Jones said the company notified the Department of Insurance that it failed to give enough notice because of a computer glitch and voluntarily offered to extend the policies.
Anthem spokesman Darrel Ng said a subset of individual customers was "inadvertently omitted from the original mailing" notifying them that their policies were being terminated. He declined to say how many Anthem customers were being notified their policies were ending.
More than 1 million cancellation notices have been sent to Californians as the Affordable Care Act begins allowing individuals to buy insurance through exchanges, Jones said. The federal law requires policies to offer minimum levels of coverage, forcing companies to terminate many existing plans.
But Jones said that under the law, insurers have another year to do so.
Last week, Blue Shield of California said it would extend 113,000 policies by an extra three months after it failed to provide 180 days' notice to customers. Blue Shield was required to provide a lengthier notification period than other insurers because it opted to switch from being regulated under the insurance commissioner's office to the state Department of Managed Health Care.
The state health care exchange, Covered California, has been accepting customers since Oct. 1 but has yet to say how many people have signed up for new policies. It is expected to announce enrollment figures Thursday.
Jones said even though both insurance companies have extended their existing coverage, policyholders who are eligible for federal premium subsidies through Covered California will likely want to choose new policies by Dec. 15 so they can begin receiving the subsidies starting Jan. 1.