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.

Insurers “can adjust their rates based on health status until 2014, to the extent state law allows,” said Jay Angoff, director of the Office of Consumer Information and Insurance Oversight at the Department of Health and Human Services.

The difficulty in preserving access to child-only insurance policies is the latest example of unintended consequences of the new law, the Patient Protection and Affordable Care Act. The problem may be solved in 2014. If Democrats can beat back Republican efforts to dismantle the law, most Americans will be required to carry health insurance, starting in 2014, and insurers will be required to accept all applicants, regardless of pre-existing conditions.

The new policy statement, issued Wednesday by Kathleen Sebelius, the secretary of health and human services, came with a fresh blast of criticism of the insurance industry.

“Unfortunately,” Ms. Sebelius said, “some insurers have decided to stop writing new business in the child-only insurance market, reneging on a previous commitment made in a March letter to ‘make pre-existing condition exclusions a thing of the past.’ ”

The White House has been tussling with insurers for months, trying to get them to provide coverage for children with cancer, autism, heart defects and other conditions.

In a letter Wednesday to the National Association of Insurance Commissioners, Ms. Sebelius said the decision of some insurers to stop issuing child-only policies was “extremely disappointing.”

But Ms. Sebelius acknowledged, “Nothing in the Affordable Care Act, or any other existing federal law, allows us to require insurance companies to offer a particular type of policy at this time.”

Insurance industry lobbyists say Ms. Sebelius mischaracterized their commitment. They denied that they had promised to continue offering child-only policies.

In a series of questions and answers intended to clarify its reading of the law, the administration said Wednesday that insurers had two options. They can enroll all children year-round, or decline to enroll all children outside the open-enrollment period.

Federal officials specifically rejected an option proposed by many insurers, which wanted to be able to accept healthy children and reject sick children outside the open-enrollment period. This option is “inconsistent with the language and intent” of the law, Ms. Sebelius said.

Insurers said they needed to bring additional healthy children into their broader insurance pools, or else premiums would go up.

Parents may seek child-only policies if they cannot afford family coverage or if they work for employers that do not offer coverage of dependents.

The administration encouraged states to set uniform open-enrollment periods for all insurers in the children’s market.

In its policy statement, the administration said, “States may set one or more open-enrollment periods for coverage for children under age 19, but cannot allow insurers to selectively deny enrollment for children with a pre-existing condition while accepting enrollment from other children outside of the open-enrollment period.”

Mr. Angoff, the Health and Human Services official, said the federal government could, by regulation, establish a uniform nationwide open-enrollment period for child-only policies. “That could get more carriers back into the market,” he said.

But Mr. Angoff said states could act faster than the federal government. “Some states, including California, Colorado, Ohio, Oregon and Washington, have already established open-enrollment periods,” he said.

On March 29, six days after President Obama signed the health care bill, Ms. Sebelius sent a sternly worded letter to insurers, saying, “Children with pre-existing conditions may not be denied access to their parents’ health insurance plan.”

Karen M. Ignagni, president of America’s Health Insurance Plans, a trade group, sent an immediate response, accepting the administration’s demand.

Robert E. Zirkelbach, a spokesman for the trade group, said Wednesday, “Health plans have upheld the commitment” by Ms. Ignagni. “Children with pre-existing conditions are able to obtain coverage on their parents’ policies,” he said.

Neither the Sebelius letter nor Ms. Ignagni’s response referred to the marketplace for child-only coverage, Mr. Zirkelbach said.

Insurers agree that if they provide insurance for a child, they cannot refuse to help pay for the treatment of pre-existing conditions. But Mr. Zirkelbach said the law “does not mandate that health plans offer coverage to all children” before 2014.