Wal-Mart Stores Inc. said Tuesday it is cutting health insurance for more of its part-time workers, as the nation’s largest private employer takes steps to rein in rising health-care costs.

The move will affect about 30,000 Wal-Mart WMT, -1.02% employees who work fewer than 30 hours a week. The loss of coverage will be a large cut in compensation for the workers, who were previously getting more than 75% of their premiums paid by Wal-Mart and will now be responsible for the costs unless they qualify for government or other subsidies.