The national League of Women Voters and the group's Kansas and Arizona chapters want to intervene in a federal lawsuit over proof-of-citizenship laws in the two states.
The groups filed their requests in a federal court case in Kansas on Thursday.
The national advocacy group Common Cause, three Arizona-based Hispanic-rights groups, and an Arizona political consultant also filed requests to intervene.
Kansas and Arizona and Secretaries of State Kris Kobach and Ken Bennett filed the lawsuit in August.
They want to force the federal government to change the national voter registration form; they say the change would help the states enforce policies that require new voters to produce citizenship papers when registering.
In addition to those groups, the American Civil Liberties Union filed a lawsuit in Shawnee County District Court to block the changes Kobach wants to make on federal voting forms.
The suit says the change would limiting voters who use a federal voter registration form to vote only in federal races and not local and state contests.
Kobach says he's not trying to impose a dual voter registration system in Kansas, but instead curb voter fraud.
He says his office is only doing planning and he hopes to avoid a system treating voters differently, based on what registration forms they use.
Since the federal voter form doesn't require people to comply with the state's proof-of-citizenship requirement, Kobach and Arizona Secretary of State Ken Bennett are trying to get the federal form changed.