Insurers are facing pressure from regulators and lawmakers about plans that offer limited choices of doctors and hospitals, a tactic the industry said is vital to keep down coverage prices in the new health law's marketplaces.

This week, federal regulators proposed a tougher review process for the doctors and hospitals in plans to be sold next year through HealthCare.gov, a shift that could force insurers to expand those networks.

Meantime, regulators in states including Washington and New Hampshire are ramping up their own scrutiny, and lawmakers in Mississippi and Pennsylvania, among others, are weighing bills that could force plans to add more hospitals and doctors.

The moves come amid complaints by some consumers that they don't have access to a broad enough range of care—such as specialists at top academic medical centers, which tend to charge insurers higher fees and aren't included in many of the new networks.

Some consumers say they will have to switch doctors with the new health-law plans. But the issue extends beyond the new policies, as insurers have been trimming the array of doctors in private Medicare Advantage coverage and losing some big health-network providers due to market clashes.