Eager to maximize coverage under the Affordable Care Act, the Obama administration has allowed large numbers of people to sign up for insurance after the deadlines in the last two years, destabilizing insurance markets and driving up premiums, health insurance companies say.

The administration has created more than 30 “special enrollment” categories and sent emails to millions of Americans last year urging them to see if they might be able to sign up after the annual open enrollment deadline. But, insurers and state officials said, the federal government did little to verify whether late arrivals were eligible.