California's public insurance exchange said Tuesday that 58,400 people have so far signed up for coverage during a special enrollment period created in response to the COVID-19 pandemic.

Starting March 20, Covered California opened up the exchange to any eligible uninsured individuals who want health coverage amid the public health emergency. The enrollment period ends June 30.

"We are living in unprecedented times, and California is doing everything it can to make sure people have access to care during this public health emergency," Covered California Executive Director Peter Lee said. "Having more people insured and protected is the right thing for California's families and helps keep everyone better off as those with insurance don't delay getting needed care."

The District of Columbia and 10 other states that run their own insurance exchanges have moved to allow uninsured people to enroll in coverage during the coronavirus pandemic. Typically, people who lose health coverage after being laid off from work or who get married or have a baby, for instance, can enroll in coverage outside of the normal annual sign-up period.

The special enrollment makes it even easier for them to do so and gives people who chose not to sign up for 2020 coverage another opportunity to enroll. The goal is to ensure that people do not put off seeking a COVID-19 test or treatment for lack of health insurance, and to ensure that those who do get sick are not saddled with huge medical bills. Some states that launched special enrollment periods have already extended the deadline to enroll.

Some health insurers, including Health Care Service Corp., have also launched special sign-up periods for certain groups. But despite pleas from state leaders and the healthcare and insurance industries, the Trump administration has refused to open the HealthCare.gov federal exchange for people in the 38 states that rely on it.

On Monday, Democratic governors in 12 states sent a letter to the heads of the HHS and CMS agencies asking them to immediately open a special sign-up period of at least 30 days so that the uninsured and underinsured could access coverage.

"Far too many of our residents are choosing to forgo coronavirus testing and treatment out of fear of the potential costs to themselves and their families at a time of increasing economic distress," they wrote. "Not only is this unacceptable, it's also dangerous as it undermines our ability as a nation to stop the spread of COVID-19."