Health insurance companies across the country are seeking and winning double-digit increases in premiums for some customers even though one of the biggest objectives of the Obama administration's health care law was to stem the rapid rise in insurance costs.

Particularly vulnerable to the high rates are small businesses and people who do not have employer-provided insurance.

In California, Aetna is proposing rate increases of as much as 22 percent, Anthem Blue Cross 26 percent and Anthem Blue Shield 20 percent for some of those policyholders. The rate requests in California are all the more striking after a 39 percent increase sought by Anthem Blue Cross in 2010 helped give impetus to the federal law, known as the Affordable Care Act, that was passed two years ago.

In other states, such as Florida and Ohio, insurers have been able to raise rates by at least 20 percent. The rate increases can amount to several hundred dollars a month.

The proposed increases compare with about 4 percent for families with employer-based policies.

Under the health care law, regulators are now required to review any request for a rate increase of 10 percent or more; the requests are posted on a federal website, healthcare.gov, along with regulators' evaluations.

The review process not only reveals the sharp disparity in the rates themselves, it also demonstrates the striking difference between places like New York, one of the 37 states where legislatures have given regulators some authority to deny or roll back rates deemed excessive, and California, which is among the states that do not have that ability.

New York, for example, recently used its sweeping powers to hold rate increases for 2013 in the individual and small group markets to under 10 percent. California can review rate requests for technical errors but cannot deny rate increases.

The double-digit requests in some states are being made despite evidence that overall health care costs appear to have slowed in recent years, increasing in the single digits annually as many people put off treatment because of the weak economy. PricewaterhouseCoopers estimates that costs may increase just 7.5 percent next year. But the companies counter that medical costs for some policyholders are rising much faster than the average, suggesting they are in a sicker population. Federal regulators contend that premiums would be higher still without the law, which also sets limits on profits and administrative costs and provides for rebates if insurers exceed those limits.

Although rates paid by employers are more closely tracked than rates for individuals and small businesses, policy experts and federal officials say the law has probably kept at least some rates lower than they otherwise would have been.