WASHINGTON — Medicare will cover annual screenings for lung cancer for older Americans with long histories of heavy smoking, the federal government said Monday in a proposal that would cover an estimated four million people, many of whom are at greatest risk for the disease.

Monday’s draft decision by the Centers for Medicare and Medicaid Services would extend coverage for CT scans to Medicare beneficiaries who smoked at least a pack a day for 30 years or the equivalent, even if they quit as long as 15 years ago. Scans would cost recipients nothing; the coverage would apply to beneficiaries through age 74.

The proposal follows a more sweeping recommendation last year by an influential government health panel that such smokers ages 55 to 80 get annual screenings, a policy shift that experts said had the potential to save 20,000 lives a year. That recommendation focused on current and former smokers at highest risk, a population of about 10 million Americans.

Under the Affordable Care Act, private insurers must cover such screenings. But the law was silent on whether Medicare had to do so. Monday’s proposal made it clear that high-risk Medicare recipients would be included.