A new federal study finds that 4.7 million children - far more than previously estimated - are eligible for Medicaid but are not enrolled in the program and have no health insurance benefits.

The finding means that two of every five uninsured children in the United States could have coverage through Medicaid, which provides comprehensive health benefits, if their parents would just apply for it.The study, published Sunday in the journal Health Affairs, said 21.2 million children ages 18 or younger were eligible for Medicaid, the federal-state program for low-income people. But, it said, 22 percent of them were not in Medicaid or any other public or private health insurance program.

The White House had estimated that 3 million children were eligible for Medicaid but not enrolled. And in January, President Clinton ordered the Department of Health and Human Services to locate such children and sign them up.

Clinton has repeatedly proposed new health programs for children and has often complained that the number of uninsured Americans is increasing because of Congress' failure to enact his proposals for universal coverage in 1994. But the study suggests that the government and low-income families have not made full use of the existing Medicaid program, which has been revised by Congress over the past decade to expand eligibility.

Those revisions have nearly doubled the number of eligible children, the study found. Children who received cash assistance through the old welfare program, Aid to Families With Dependent Children, were automatically enrolled in Medicaid. But teenagers and children who became eligible for Medicaid because of program expansions were less likely to be enrolled.