WASHINGTON — Under pressure from the White House, health insurance companies said Tuesday that they would comply with rules to be issued soon by the Obama administration requiring them to cover children with pre-existing medical problems.

“Health plans recognize the significant hardship that a family faces when they are unable to obtain coverage for a child with a pre-existing condition,” said Karen M. Ignagni, president of America’s Health Insurance Plans, a trade group. Accordingly, she said, “we await and will fully comply with” the rules.

Ms. Ignagni made the commitment in a letter to Kathleen Sebelius, the secretary of health and human services, who had said she feared that some insurers might exploit a possible ambiguity in the new health care law to deny coverage to some sick children.

The White House immediately claimed victory.

In a Twitter message, Robert Gibbs, the White House press secretary, scored the tug of war as “Kids 1, insurance 0.”