In lawsuits filed in federal courts in Pennsylvania, Nevada, Arizona and Ohio, Democrats argued that Trump and Republican Party officials were mounting a "campaign of vigilante voter intimidation" that violated the 1965 Voting Rights Act and an 1871 law aimed at the Ku Klux Klan.
"Trump has sought to advance his campaign's goal of 'voter suppression' by using the loudest microphone in the nation to implore his supporters to engage in unlawful intimidation," the Ohio Democratic Party wrote in a legal filing. Similar language was used in the other lawsuits.
The Trump campaign did not respond to a request for comment.
Since August, Trump has urged his supporters to monitor polling locations on Election Day for signs of possible voting fraud, often urging them to keep a close eye on cities like Philadelphia and St. Louis that have high minority populations.
Campaigning in Ohio, Democratic presidential nominee Hillary Clinton said Trump was hoping to discourage people from participating in the election.
"His whole strategy is to suppress the vote. Lots of noise. Lots of distractions," Clinton said in Cleveland.
Democrats are also trying to stop the Republican National Committee from working with the Trump campaign or state parties on poll monitoring, arguing in a separate case that a long-standing court order prevents the national party organization from engaging in "ballot security" measures.
In a motion filed on Monday in that case, the RNC said it was not involved in poll watching but was working to support Trump in other areas. "That is evidence of politics, not wrongdoing," the RNC said.
Many states allow campaigns and political parties to monitor balloting, although they often face restrictions. In Pennsylvania, for example, poll watchers must be formally certified by the local election board and must be registered voters in the county where they are working. The state Republican party has sued to remove those restrictions.
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 behaviour.
Democrats also sued Republican operative Roger Stone, a long-time Trump ally who is organizing an exit-polling effort. Democrats said the true purpose of the project, called Stop the Steal, was to intimidate minority and urban voters.
Stone told Reuters that his project was designed to ensure that electronic voting machines were working properly.
On Stop the Steal's website, Stone says Clinton's Democrats "intend to flood the polls with illegals. Liberal enclaves already let illegals vote in their local and state elections and now they want them to vote in the Presidential election."
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.
"Since we are only talking to voters after they have voted, how can we be intimidating them?" Stone said.
