ST. PAUL — Republican backers of requiring a photo ID to vote in Minnesota say they’ll try to take the issue to voters themselves next year after Gov. Mark Dayton vetoed a bill with the requirement.

Rep. Mary Kiffmeyer and Sen. Scott Newman said Tuesday they’ll push the constitutional amendment in next year’s legislative session. If passed by the Legislature, the amendment would be on the ballot in the November 2012 election.

Backers said it would bring more integrity to the state’s election system. When Dayton vetoed the Legislature’s bill last month, he said backers failed to show that voter fraud is a widespread problem in Minnesota.

But Dayton cannot block constitutional amendments from the ballot. Voters next year will already be voting on an amendment to define marriage in the Minnesota Constitution.