WASHINGTON  The Obama administration, aiming to encourage health insurance companies to offer child-only policies, said Wednesday that they could charge higher premiums for coverage of children with serious medical problems, if state law allowed it.

Earlier this year, major insurers, faced with an unprofitable business, stopped issuing new child-only policies. They said that the Obama administration’s interpretation of the new health care law would allow families to buy such coverage at the last minute, when children became ill and were headed to the hospital.

In September, the administration said that insurers could establish open-enrollment periods  for example, one month a year  during which they would accept all children.

Now, on Wednesday, the administration, answering a question raised by many insurers, said they could charge higher premiums to sick children outside the open-enrollment period, if state laws allowed such underwriting, as many do.