Oregon’s insurance regulator has approved big premium increases sought by health plans for 2016 under the health law, and in some cases ordered higher raises than insurers requested, signaling that the cost of insurance for people who buy it on their own could jump after two years of relatively modest growth.

Around the U.S., the biggest insurers have proposed hefty premium increases for the year ahead, based on what they say they now know about the costs of covering people newly enrolled under the Affordable Care Act. Supporters of the law have been counting on state regulators to rein in hefty premium increases for the law’s third year in full effect.

But in Oregon, the first state to announce final 2016 rates, Insurance Commissioner Laura Cali approved an average 25.6% increase for Moda Health Plan Inc., the biggest plan on the state’s health exchange. She also gave a green light to average increases of 30% or more for four smaller companies. And she required plans that hadn’t attempted to raise rates to do so anyway, including Kaiser Foundation Health Plan of the Northwest, by an average of 8.3%.

Ms. Cali said the changes were necessary for plans to stay afloat. State actuaries had reviewed claims incurred in 2014 and concluded they exceeded premiums collected that year by $127 million, or an average of $624 a person who signed up for insurance on their own, she said.