A Wake County judge granted a temporary restraining order keep the law from going into effect January 1.
In the lawsuit, Cooper says the law - known as Senate Bill 4 - that takes the control of the State Board of Elections from the governor and gives it to the General Assembly is unconstitutional.
The changes convert the state elections board from one that governors have controlled into a bipartisan body with equal numbers of Republicans and Democrats. County election boards would have two members from each party, rather than the current three members with a majority from the governor's party.
"This complex new law passed in just two days by the Republican legislature is unconstitutional and anything but bipartisan. A tie on a partisan vote would accomplish what many Republicans want: making it harder for North Carolinians to vote. It will result in elections with longer lines, reduced early voting, fewer voting places, little enforcement of campaign finance laws, indecision by officials and mass confusion," Cooper said.
Wake County Superior Court Judge Don Stephens ruled Friday that the risk to free and fair elections justified stopping the law from taking effect this weekend until it could be reviewed more closely. Stephens plans to review the law Thursday.
"If I do not grant the temporary restraining order, the State Board of Elections will be disbanded. That will not maintain the status quo," Stephens said.
Stephens had a testy exchange with Noah Huffstetler III, a Republican attorney:
Judge Stephens: "Let me just tell you this. If I do nothing, the State Board of Elections will not exist on Monday morning or Tuesday morning. I mean, how will they join this action?"
Huffstetler: "Well, you honor, they are in the process of combining even as we speak. Again, that would be the party that would have the right to do this."
Judge Stephens: "What party? Combined into what? The new agency whose creation is alleged to be unconstitutional?"
"They've had 13 bills that they're introduced, reversed as unconstitutional," said left-leaning attorney Michael Weisel on the GOP's track record of enacting controversial legislation. "That's a pretty unbelievable record. They don't seem to listen to their staff attorneys to say perhaps you're overreaching here and this may not be a constitutional bill.
"If you create a board that is not controlled by the executive, because this is an executive function as stated, then you have taken away the right to free and fair elections," Weisel added. "I think the way that the judge noted was the way the board was set up, what was the remedy if the board could not agree to early voting hours? Or registration time frames."
Republican Senate Leader Phil Berger issued a statement after learning of the lawsuit:
"Given the recent weeks-long uncertainty surrounding his own election, the governor-elect should understand better than anyone why North Carolinians deserve a system they can trust will settle election outcomes fairly and without the taint of partisanship. Roy Cooper's effort to stop the creation of a bipartisan board with an equal number of Democrats and Republicans to enforce elections and ethics laws may serve his desire to preserve his own political power, but it does not serve the best interests of our state."
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Cooper's lawsuit makes good on his previous threats to take Republicans to court over laws passed during two December special sessions. Another of the laws requires Cooper's Cabinet choices to be confirmed by legislators. The state constitution gives the Senate the ability to "advise and consent" to the governor's appointees by a majority vote, but that provision hadn't been used in at least several decades.
NCGOP Chairman Robin Hayes also responded to Cooper's action.
"After a close and divisive election, instead of seeking a bipartisan review of election and ethics issues, governor-elect Cooper has chosen to go into full partisan attack mode," Hayes said. "Instead of seeking real and reasonable bipartisan solutions that provide confidence for everyone in the nation that North Carolina ethics and election decisions are partisan free, he instead shows exactly why this change to a bipartisan system is needed."
NCDP Chairwoman Patsy Keever countered, calling Republicans hypocrites.
"It is hypocritical for Republicans to hijack the bipartisan mantle in abolishing the N.C. Board of Elections. Calling a special session under the guise of hurricane relief, GOP leadership sprang a surprise bill to abolish the board of elections," Keever said. "They didn't consult Governor-elect Cooper. They didn't consult Democratic legislators. They introduced the bill and rammed it through on the same day with little debate. What kind of bipartisanship is that?
"The truth is, the state board of elections stood up to attempts by Pat McCrory to bully elections board members into reversing the outcome of McCrory's historic loss," Keever added. "The reward they got for doing their job? McCrory and the legislature attempted to abolish the elections board. North Carolina is better than this."
The Associated Press contributed to this report