Sen. Ted Cruz Rafael (Ted) Edward CruzLoeffler calls for hearing in wake of Netflix's 'Cuties' Health care in the crosshairs with new Trump Supreme Court list 'Parks and Rec' cast members hosting special reunion to raise money for Wisconsin Democrats MORE (R-Texas) on Monday said he would offer an amendment to the Senate immigration bill to counteract a Supreme Court decision striking down state laws requiring voters to prove their citizenship.

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Cruz's amendment, which he plans to attach to the bipartisan Gang of Eight bill being debated this week in the Senate, would allow states to require IDs before voters register under the federal "Motor Vehicle" voter registration law.

The high court on Monday overturned an Arizona law requiring people to prove their citizenship if they wanted to register through that law. In a 7-2 vote, the court ruled in the case of Arizona v. The Inter Tribal Council of Arizona, Inc. that state law was trumped by federal law and Arizona could not require voters to provide additional information.

"The U.S. Supreme Court ruled today that the federal 'motor voter' law preempts Arizona’s proof-of-citizenship requirement for voter registration," Cruz wrote on his Facebook page on Monday, criticizing the court’s decision. "This hole in federal statutory law allows non-citizens to register and thereby encourages voter fraud.

“I will file a commonsense amendment to the immigration bill that permits states to require I.D. before registering voters," he vowed.

Cruz’s amendment will likely intensify the Senate debate over the immigration reform bill.

Cruz has been a vocal critic of the bill, which provides a pathway to citizenship for the nation’s 11 million illegal immigrants and tightens border security.

Cruz and other conservative lawmakers have derided those proposals as amnesty and say they will oppose the measure unless more stringent border restrictions are enacted.

Arizona has been on the frontlines of the debate over citizenship and immigration, with the court striking down a state law last year that allowed law enforcement to arrest those they suspected of being illegal immigrants.

This story was updated at 4:33 p.m.