The largest health insurer in Texas wants to hike premiums for Obamacare plans by nearly 60 percent, the latest evidence that consumers may see steep cost increases this year under President Obama's healthcare law.

Blue Cross Blue Shield of Texas has requested hikes it says could affect nearly 603,000 Texans buying health plans through healthcare.gov, the insurance marketplace set up under Obamacare. The rates have yet to be finalized and Blue Cross could choose to ramp them down, but the Obama administration lacks the authority to force the insurer to do so.

The rate hike was announced as insurers in other states are also requesting double-digit increases that are larger than those seen in previous years, in part because next year they'll no longer receive extra federal funds to help them pay for sicker, more expensive customers.

Because insurers can no longer deny someone coverage due to their pre-existing condition, many are arguing they have an influx of patients with more expensive healthcare needs in the Obamacare marketplaces, prompting some, including United, to withdraw from the marketplaces completely.

Blue Cross Blue Shield wants to charge between 57.33 percent and 59.35 percent more for two of its Blue Advantage Plus plans, according to filings on Healthcare.gov. A Blue Advantage Health Maintenance Organization Plan is asking for a 58.6 percent hike.

Blue Cross Blue Shield of Texas said its requested rates are based on strong financial principles, science and data. "It's also important to understand the magnitude of the losses… experienced in the individual retail market over the past two years," the company said in a statement, adding that it lost $592 million last year and $416 million in 2014.