WASHINGTON — Millions of people facing the cancellation of health insurance policies will be allowed to buy catastrophic coverage and will be exempt from penalties if they go without insurance next year, the White House said Thursday night.

Kathleen Sebelius, the secretary of health and human services, disclosed the sudden policy shift in a letter to Senator Mark Warner, Democrat of Virginia, and five other senators.

It was another effort by President Obama to cushion the impact of the health care law and minimize political damage to himself and Democrats in Congress who adopted the law in 2010 over solid Republican opposition.

In recent weeks, insurers have told many people that their insurance policies were being canceled because they did not comply with the minimum coverage requirements of the law. Insurers usually offer to replace the coverage with new policies that do comply, providing more benefits at higher cost.