WASHINGTON — A new front is opening in the battle to restore so-called net neutrality rules: state legislatures.

Lawmakers in at least six states, including California and New York, have introduced bills in recent weeks that would forbid internet providers to block or slow down sites or online services. Legislators in several other states, including North Carolina and Illinois, are weighing similar action.

They are responding to the Federal Communications Commission’s vote last month to end regulations that barred internet service providers from creating slow and fast lanes for different sites and services. The new policy will go into effect in the coming weeks.

By passing their own law, the state lawmakers say, they would ensure that consumers would find the content of the choice, maintain a diversity of voices online and protect businesses from having to pay fees to reach users. And they might even have an effect beyond their states. California’s strict auto emissions standards, for example, have been followed by a dozen other states, giving California major sway over the auto industry.