WASHINGTON – After battling President Obama’s health care overhaul for the better part of a year, the insurance industry said Monday it won’t try to block his efforts to fix a potentially embarrassing glitch in the new law.

In a letter to Health and Human Services Secretary Kathleen Sebelius, the industry’s top lobbyist said insurers will accept new regulations to dispel uncertainty over a guarantee that children with medical problems can get coverage starting this year.

Quick resolution of the doubts was a win for Obama — and a sign that the industry has no stomach for another war of words with a president who deftly used double-digit rate hikes by the companies to revive his sweeping health care legislation.

“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,” Karen Ignagni, president of America’s Health Insurance Plans, said in a letter to Sebelius. Ignagni said that the industry will “fully comply” with the regulations, expected within weeks.

The industry’s response followed a sternly worded letter from Sebelius earlier in the day. In it, she tried to put an end to questions about the law’s intent and wording.

“Now is not the time to search for nonexistent loopholes that preserve a broken system,” Sebelius wrote to Ignagni.

Sebelius specified that a child with a pre-existing medical problem may not be denied access to parents’ coverage under the new law. Furthermore, insurers will not be able to insure a child but exclude treatments for a particular medical problem.

If the uncertainty had persisted, some parents and children may have had to wait a long time for coverage. The law’s ban on denying coverage to any person on account of a health condition doesn’t take effect until 2014.