(Reuters) - Civil rights groups in Tennessee have asked a federal court to block enforcement of a new state law that threatens to impose new penalties on voter-registration groups if they file too many incomplete forms.

The state’s Republican Governor, Mike Lee, signed the bill passed by the Republican-dominated legislature on Thursday, saying it would help ensure the integrity of elections.

The law imposes fines on groups that file more than 100 incomplete voter registration forms and threatens paid workers who file more than 100 forms without state training with up to a year in jail.

U.S. politicians, particularly Republicans, have long cited concerns about fraud to justify laws restricting access to polls. But independent researchers have documented only a handful of cases over the years, and many Democrats and civil rights groups say the restrictions disproportionately affect poorer voters and members of minority groups.

The Tennessee Conference of the NAACP and the three other civil rights group sued the state in U.S. District Court in Nashville, calling the law an effort at voter suppression and asking a judge to stop its enforcement. They said it will hurt their work enrolling African-Americans and members of other minority groups, many of whom tend to vote for Democrats, in a state that already has one of the lowest election turnout rates in the nation.

The Tennessee lawsuit says the law’s wording is so vague it is not clear whether registering a voter named James under his nickname Jim would be penalized.

“This is nothing more than a thinly veiled attempt to discourage and deter people from helping others to register to vote,” Kristen Clarke, president and executive director of the Lawyers’ Committee for Civil Rights Under Law, the group that helped filed the lawsuit, said in a statement.

The law exempts unpaid volunteers from the requirements, but the groups behind the lawsuit say it is unclear whether their use of paid staff to oversee volunteers will make them subject to the penalties.

Tennessee Secretary of State Tre Hargett, a Republican, did not respond to a request for comment. His office has previously said that thousands of incomplete forms have created difficulties for election officials.

The voter registration issue came to the fore again around last year’s elections for the U.S. Congress, and many of the Democratic 2020 presidential hopefuls have made attacks on voting restrictions part of their campaigns.

A North Carolina Republican political operative was arrested in February and charged with running an absentee ballot fraud scheme that led the state to order the rerun of a congressional election.