SACRAMENTO, Calif.—The state of California has agreed to mail voter registration forms to nearly 4 million people who have signed up for insurance through its health care exchange after a threat of a lawsuit, the American Civil Liberties Union said Monday.

The ACLU of California and others said they threatened to sue the state for failure to comply with the National Voter Registration Act, also called the Motor Voter Act. The law is designed to make it easier for voters to register by requiring there to be opportunities to apply at offices that provide public services.

The ACLU said Covered California had provided no opportunities since it launched Oct. 1. The mailings must be completed by May 5.

The 19-page agreement also commits the state to develop procedures by this fall to ensure that all insurance applicants have an opportunity to register to vote, whether they apply in person, online, by phone or mail.

Dale Ho, director of the ACLU's Voting Rights Project, called the settlement a warning to other health exchanges that he says have not provided voter registration opportunities, such as Nevada, Hawaii, Washington and Washington, D.C.

"It's time to end the foot-dragging," Ho said. "States have had months to make voter registration available through their health exchanges. A delay in offering voter registration is a delay for democracy."

The agreement was approved by Covered California's board and signed by California Secretary of State Debra Bowen and Peter Lee, Covered California's executive director.

In its first months, Covered California was focused on its core function of getting its new insurance marketplace up and running, "including building a state agency and online enrollment portal from scratch," spokeswoman Anne F. Gonzales said Monday.

"Under this agreement, we will be in full compliance through all application channels by the first day of open enrollment in fall 2014," Gonzales said. "Voter registration cards will be included in all paper applications, and a voter registration application will be built into the online application, which will be seen by consumers early in the application process."

Consumers will be able to get voter registration information from Covered California by phone and in person.

The ACLU and public policy activist groups Demos and Project Vote told Bowen on March 5 that California failed to comply with the law and threatened to sue.

The National Voter Registration Act of 1993 requires states to provide opportunities to vote to people who are applying for or renewing driver's licenses. The ACLU threatened to sue under a provision that requires voter registration opportunities at state offices that provide public assistance and offices that provide state-funded programs primarily engaged in services for people with disabilities.