WASHINGTON — With many people still stymied in their efforts to buy insurance under the new health-care law, the Obama administration said Thursday that it would extend an expiring program for people with cancer, heart disease and other serious illnesses.

The extension provides a one-month reprieve for the program, known as the Pre-Existing Condition Insurance Plan.

About 135,000 people nationwide have enrolled in the program, which is essentially a high-risk pool sponsored by the federal government.

About 443 Washington state residents have coverage through the federal plan; another 3,675 have coverage under a state-run high-risk pool called the Washington State Health Insurance Pool (WSHIP).

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Although the state pool is not accepting new applicants, those who currently have coverage can continue until Dec. 31, 2017; Medicare recipients in the pool won’t be discontinued.

The federal program was to end Dec. 31. Congress had assumed that it would no longer be needed because insurers would be prohibited from denying coverage, or charging higher rates, to people based on their health status or medical history.

Despite improvements in the website for the federal insurance marketplace, HealthCare.gov, some people say they still have difficulty using it to enroll in health plans.

Consumers have also had difficulty using websites for some insurance exchanges run by states.

Aaron Albright, a spokesman at the federal Centers for Medicare and Medicaid Services, said Thursday, “As part of our efforts to smooth the transition to the marketplaces for those seeking coverage that begins in January, we are taking steps to ensure that Americans enrolled in the federal PCIP insurance plan will not face a lapse when the new year begins.”