The Senate has also advanced Secretary of State Kris Kobach's proposal to give his office the power to prosecute election fraud cases.
But debate on the measure exposed a split among Republicans who control the Legislature.
The Senate gave the bill first-round approval on a voice vote.
It's expected to pass in a final vote today and go to the House.
Kobach says county prosecutors are usually too busy to pursue election fraud cases.
But critics say there's not enough election fraud to justify such a move.
The measure also boosts the penalties for election crimes. Senators considered an amendment to strip out the provision giving Kobach's office prosecutorial power.
The vote was 23-15 against the amendment. But eight Republicans supported it.
