The Kansas House has approved Secretary of State Kris Kobach’s proposal to require first-time voters to prove their U.S. citizenship starting June 15.

The vote Wednesday was 72-51. The measure goes next to the Senate.

Kansas already has the rule for people registering to vote for the first time in the state, but it doesn’t take effect until January 2013. Kobach wants the rule in place for the normal surge of voter registrations ahead of this year’s presidential election. Critics argue it will suppress voter turnout.

The House approved an earlier version of Kobach’s plan in February, but the measure stalled in a Senate committee. Kobach’s allies hope senators will vote on the latest version without sending it to committee.