The lawsuit, which was filed last week in federal court, also says the congressional redistricting plan should include at least two majority-minority districts.
Majority-minority districts contain at least 50 percent minorities with the goal of electing a minority representative.
Sen. Fletcher Hartsell, R-Cabarrus, said the lawsuit's goal is to force lawmakers to comply with the redistricting requirements of the N.C. Constitution.
Hartsell said that among these requirements is the need to follow a one-man, one-vote proportion of representation.
But Senate Democrats said the suit is a waste of taxpayer money.
"Our folks feel there's no basis for the lawsuit," said Sen. Ellie Kinnaird, D-Orange. "The map is racially balanced."
Kinnaird said the suit likely would get dismissed quickly but a hearing would last for months.
The Republican Party filed the suit Nov. 13 against House Speaker Jim Black, D-Mecklenburg, challenging how he refused to allow amendments to the plan.
The Senate Congressional Redistricting Committee discussed two alternative plans Tuesday, further delaying the redistricting process. The House approved a plan Thursday.