J. Scott Applewhite, Associated Press
In this March 23, 2010 file photo, Marcelas Owens of Seattle, left, Rep. John Dingell, D-Mich., right, and others, look on as President Barack Obama signs the health care bill in the East Room of the White House in Washington.

WASHINGTON — The health insurance industry says the president's offer to fend off millions of cancellations comes too late — and may raise premiums.

America's Health Insurance Plans is the main industry trade group. The group says members have already set premiums for next year based on the assumption that many people with current individual coverage will shift into the new markets created under the health care law.

Plans sold under the law offer broader benefits and stronger financial protections than many current individual market policies.

Karen Ignagni is president of the industry group. She says allowing people to keep plans that don't comply with the law could destabilize the market and lead to higher premiums.

That's because younger, healthier people might stay out of the new markets.