With early voting under way, civil rights groups have said they have heard isolated reports of self-described poll monitors photographing voters and engaging in other intimidating behavior.
The lawsuits were filed beginning Sunday in Ohio, Pennsylvania, Nevada and Arizona.
"The Party is threatened with immediate and irreparable injury if the vigilante voter intimidation campaign by Trump, Stone, and their co-conspirators succeeds in disrupting or changing the results of the election by means of an unlawful conspiracy", the Democrats' lawsuit says.
Democrats are accusing Republicans and Donald Trump's presidential campaign of conspiring to intimidate voters in at least four key states.
The lawsuits argue that the Trump campaign, along with the nominee's close confidant Roger Stone and state Republican party officials, is "conspiring to threaten, intimidate, and thereby prevent minority voters in urban neighborhoods from voting", citing Trump's continuing efforts to recruit "election observers" and Stone's plans, as revealed by the Guardian, to conduct unorthodox "exit polling" on election day, as evidence of potentially "virulent harassment".
"In the months leading up to the 2016 election, Trump has made an escalating series of statements, often racially tinged, suggesting that his supporters should go to particular precincts on Election Day and intimidate voters", the OH lawsuit alleged. But a number of polling and election law experts cast doubts on the methodology and suggested the process could be a smokescreen for voter intimidation.
Ohio Republican Party spokeswoman Brittany Warner called the lawsuit "a publicity stunt" and said the party is not involved in such voter intimidation.
Stone told the Guardian last week his group "Stop The Steal" planned to conduct exit polling in nine major cities in swing states, ostensibly to counter "election theft" and gauge the accuracy of electronic voting machines.
"We are not coordinating with the Trump campaign, the Republican National Committee or the individual Republican State Committees", Stone wrote in the email. The former Richard Nixon adviser said the polling was not being coordinated with the Trump campaign or the RNC.
Stone said the 1,400 people across the United States who volunteered for the project had been instructed to use neutral language and only approach people after they had voted.
Trump's Nevada campaign has been recruiting poll watchers, but he said they're trained to act within the law. The suit says the state Republican Party is essentially an arm of Trump's campaign and the campaign and its backers have been organizing "citizen journalists" and "poll watchers" to flood minority-heavy polling sites on November 8.
Arizona Democratic Party Chairwoman Alexis Tameron said the party is anxious that "rogue actors" will scare off voters.
"The Nevada Republican Party is committed to holding free, fair, and open elections throughout the state of Nevada", he said in a statement.