Health insurance companies around the country are seeking rate increases of 20 to 40 percent or more, saying their new customers under the Affordable Care Act turned out to be sicker than expected. Federal officials say they are determined to see that the requests are scaled back.

Blue Cross and Blue Shield plans — market leaders in many states — are seeking rate increases that average 23 percent in Illinois, 25 percent in North Carolina, 31 percent in Oklahoma, 36 percent in Tennessee and 54 percent in Minnesota, according to documents posted online by the federal government and state insurance commissioners and interviews with insurance executives.

President Obama said consumers should put pressure on state insurance regulators to scrutinize the proposed increases.

It is far from certain how many of the rate increases will hold up on review, or how much they might change. But the proposals, buttressed with reams of actuarial data, are fueling fierce debate about the effectiveness of the health law.

Sylvia Mathews Burwell, secretary of health and human services, said federal subsidies would soften the impact of any rate increases. Of the 10.2 million people who obtained coverage through federal and state marketplaces this year, 85 percent receive subsidies in the form of tax credits to help pay premiums.