WASHINGTON — Fresh problems for Obamacare: The largest health insurer in Texas wants to raise its rates on individual policies by an average of nearly 60 percent, a new sign that President Obama’s overhaul hasn’t solved the problem of price spikes.

Texas isn’t alone. Citing financial losses under the health care law, many insurers around the country are requesting bigger premium increases for 2017. That’s to account for lower-than-hoped enrollment, sicker-than-expected customers and problems with the government’s financial backstop for insurance markets. The national picture will take weeks to fill in. With data available for about half the states, premium increases appear to be sharper, but there are also huge differences between states and among insurers.

Health insurance is priced locally. A recent analysis of nine states by the consulting firm Avalere Health found that average premium increases for the most popular kind of plan ranged from 5 percent in Washington state to 44 percent in Vermont.

Millions of customers will be shielded from price hikes by government subsidies, which typically cover more than 70 percent of the premiums. People who don’t have access to a workplace plan can buy a policy directly on the health law’s marketplaces.

But many consumers aren’t eligible for the income-based subsidies and get no such protection. That demographic includes small business owners, self-employed people and early retirees. Under the law, most Americans are required to have health insurance or risk being fined.

Blue Cross Blue Shield of Texas has about 603,000 individual policyholders. In a recent filing with federal regulators, the company said it is seeking increases averaging from 57.3 percent to 59.4 percent across its individual market plans.

In a statement, Blue Cross Blue Shield of Texas says it lost $592 million last year and $416 million in 2014.

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