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 for consumers.

Particularly vulnerable to the high rates are small businesses and people who do not have employer-provided insurance and must buy it on their own.

In California, Aetna is proposing rate increases of as much as 22 percent, Anthem Blue Cross 26 percent and Blue Shield of California 20 percent for some of those policy holders, according to the insurers’ filings with the state for 2013. These rate requests are all the more striking after a 39 percent rise sought by Anthem Blue Cross in 2010 helped give impetus to the law, known as the Affordable Care Act, which was passed the same year and will not be fully in effect until 2014.

 In other states, like Florida and Ohio, insurers have been able to raise rates by at least 20 percent for some policy holders. 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 Web site, 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, well below the rate increases being sought by some insurers. But the companies counter that medical costs for some policy holders 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.

Critics, like Dave Jones, the California insurance commissioner and one of two health plan regulators in that state, said that without a federal provision giving all regulators the ability to deny excessive rate increases, some insurance companies can raise rates as much as they did before the law was enacted.

“This is business as usual,” Mr. Jones said. “It’s a huge loophole in the Affordable Care Act,” he said.

While Mr. Jones has not yet weighed in on the insurers’ most recent requests, he is pushing for a state law that will give him that authority. Without legislative action, the state can only question the basis for the high rates, sometimes resulting in the insurer withdrawing or modifying the proposed rate increase.

The California insurers say they have no choice but to raise premiums if their underlying medical costs have increased. “We need these rates to even come reasonably close to covering the expenses of this population,” said Tom Epstein, a spokesman for Blue Shield of California. The insurer is requesting a range of increases, which average about 12 percent for 2013.

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

“There’s no question that review of rates makes a difference, that it results in lower rates paid by consumers and small businesses,” said Larry Levitt, an executive at the Kaiser Family Foundation, which estimated in an October report that rate review was responsible for lowering premiums for one out of every five filings.

Federal officials say the law has resulted in significant savings. “The health care law includes new tools to hold insurers accountable for premium hikes and give rebates to consumers,” said Brian Cook, a spokesman for Medicare, which is helping to oversee the insurance reforms.

“Insurers have already paid $1.1 billion in rebates, and rate review programs have helped save consumers an additional $1 billion in lower premiums,” he said. If insurers collect premiums and do not spend at least 80 cents out of every dollar on care for their customers, the law requires them to refund the excess.

As a result of the review process, federal officials say, rates were reduced, on average, by nearly three percentage points, according to a report issued last September.

In New York, for example, state regulators recently approved increases that were much lower than insurers initially requested for 2013, taking into account the insurers’ medical costs, how much money went to administrative expenses and profit and how exactly the companies were allocating costs among offerings. “This is critical to holding down health care costs and holding insurance companies accountable,” Gov. Andrew M. Cuomo said.

While insurers in New York, on average, requested a 9.5 percent increase for individual policies, they were granted an increase of just 4.5 percent, according to the latest state averages, which have not yet been made public. In the small group market, insurers asked for an increase of 15.8 percent but received approvals averaging only 9.6 percent.

But many people elsewhere have experienced significant jumps in the premiums they pay. According to the federal analysis, 36 percent of the requests to raise rates by 10 percent or more were found to be reasonable. Insurers withdrew 12 percent of those requests, 26 percent were modified and another 26 percent were found to be unreasonable.

And, in some cases, consumer advocates say insurers have gone ahead and charged what regulators described as unreasonable rates because the state had no ability to deny the increases.

Two insurers cited by federal officials last year for raising rates excessively in nine states appear to have proceeded with their plans, said Carmen Balber, the Washington director for Consumer Watchdog, an advocacy group. While the publicity surrounding the rate requests may have drawn more attention to what the insurers were doing, regulators “weren’t getting any results by doing that,” she said.

Some consumer advocates and policy experts say the insurers may be increasing rates for fear of charging too little, and they may be less afraid of having to refund some of the money than risk losing money.

Many insurance regulators say the high rates are caused by rising health care costs. In Iowa, for example, Wellmark Blue Cross Blue Shield, a nonprofit insurer, has requested a 12 to 13 percent increase for some customers. Susan E. Voss, the state’s insurance commissioner, said there might not be any reason for regulators to deny the increase as unjustified. Last year, after looking at actuarial reviews, Ms. Voss approved a 9 percent increase requested by the same insurer.

“There’s a four-letter word called math,” Ms. Voss said, referring to the underlying medical costs that help determine what an insurer should charge in premiums. Health costs are rising, especially in Iowa, she said, where hospital mergers allow the larger systems to use their size to negotiate higher prices. “It’s justified.”

Some consumer advocates say the continued double-digit increases are a sign that the insurance industry needs to operate under new rules. Often, rates soar because insurers are operating plans that are closed to new customers, creating a pool of people with expensive medical conditions that become increasingly costly to insure.

While employers may be able to raise deductibles or co-payments as a way of reducing the cost of premiums, the insurer typically does not have that flexibility. And because insurers now take into account someone’s health, age and sex in deciding how much to charge, and whether to offer coverage at all, people with existing medical conditions are frequently unable to shop for better policies.

In many of these cases, the costs are increasing significantly, and the rates therefore cannot be determined to be unreasonable. “When you’re allowed medical underwriting and to close blocks of business, rate review will not affect this,” said Lynn Quincy, senior health policy analyst for Consumers Union.

The practice of medical underwriting — being able to consider the health of a prospective policy holder before deciding whether to offer coverage and what rate to charge — will no longer be permitted after 2014 under the health care law.