The federal lawsuits in four battleground states — Arizona, Nevada, Ohio and Pennsylvania — arrived just over a week before Election Day and amid polls showing a tightening campaign between Trump and Hillary Clinton, his Democratic opponent. In these lawsuits, officials accuse Trump’s campaign and his backers of what the Ohio complaint describes as a “coordinated campaign of vigilante voter intimidation.”

Trump has repeatedly described the election as “rigged” without offering any evidence, claims that have worried officials preparing for potential unrest or violence on Election Day. Party leaders and officials across the country have also expressed concerns about voter intimidation and problems at the polls.

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In the Ohio lawsuit, the state Democratic Party asked a federal judge to stop the Trump campaign, state party officials and a group associated with Trump supporter Roger Stone from sending people not officially appointed as poll watchers to voting locations.

Attorneys for the Ohio Republican Party, the Trump campaign and Stone did not immediately file court documents responding to that lawsuit, but they were ordered to respond by the end of Wednesday.

“This is nothing more than a publicity stunt from the Ohio Democratic Party,” Brittany Warner, a spokeswoman for the Ohio GOP, said in a statement. “The arguments cited are not at all related to our official operations at the Ohio Republican Party. Republican leadership in Ohio has created opportunities for greater ballot access and in no way would we ever be involved in the intimidation of voters. Our attorneys are working to prepare the appropriate response.”

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In a statement, Stone called the lawsuit “bogus” and said that his group, Stop the Steal, “is conducting a neutral, scientifically based exit poll” that would only involve interviews after people cast ballots.

“We are not coordinating with the Trump campaign, the Republican National Committee or the individual Republican state committees,” Stone said. “We are not engaged in poll watching. We seek only to determine if the election is honestly and fairly conducted and to provide an evidentiary basis for a challenge to the election if that is not the case.”

The Trump and Clinton campaigns did not respond to requests for comment about the lawsuits, nor did the Republican National Committee or Democratic National Committee.

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Voting rights advocates, who are also expecting some confusion on Election Day because of a wave of stricter election laws still facing litigation, say they are already receiving more calls about problems at polls.

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“When people call and tell us they’re experiencing something they deem hostile, we take that seriously,” said Kristen Clarke, president of Lawyers’ Committee for Civil Rights Under Law, which has seen increased calls to their offices this election cycle.

Last week, Clarke said that her group received calls about Trump supporters using bullhorns to shout at Clinton supporters and voters outside an early polling location in West Palm Beach, Fla. Video posted by the news outlet ProPublica showed a Trump supporter on a bullhorn yelling, “How many Syrian refugees, Muslim refugees, are you taking into your home?”

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Clarke said her organization complained to authorities, who then ordered the individuals to move farther away from the polling site.

These issues were also likely to continue playing out in court. In another potentially key legal filing this week, a federal judge on Monday ordered the Republican National Committee — which is still under a consent decree issued in 1982 — to turn over “all agreements” between the committee and the Trump campaign “regarding voter fraud, ballot security, ballot integrity, poll watching, or poll monitoring.”

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This case could have huge ramifications on the last-minute strategies of both parties, said election law expert Rick Hasen of the University of California at Irvine.

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“That could provide valuable information to the Democratic Party and others in terms of the Trump poll-watching plans,” Hasen said Tuesday. “So that single discovery order is probably the biggest election law victory for Democrats in the last month.”

While Hasen said that he remains most concerned about an Internet-based attack that takes out vital online infrastructure on Election Day, he said that he is also still concerned about voter intimidation and rogue Trump supporters getting into confrontations.

But Hasen said Democrats hoping to extend the consent decree, which restricts the Republican committee’s efforts to challenge voters at the polls, would benefit if they can get the Trump campaign and Republican officials on the “on record denying poll watching and intimidation” plans for Election Day if those things wind up happening.

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“The 2016 election and the conduct of Trump and [the] RNC on Election Day are going to be very relevant to that question of whether to extend the consent decree,” he said.

Millions have already voted, and both campaigns are still making a frantic push toward the finish line. Trump campaign officials have said that they are “on the offensive everywhere” and are trying to make a push in traditionally Democratic states, while Clinton officials and surrogates are trying to boost turnout in big cities while also seeking to flip Arizona.

In their lawsuits filed earlier this week, Democrats pointed to Trump’s repeated suggestions — offered without evidence — that the election will be “rigged,” his unsubstantiated claims of “large-scale voter fraud” and his calls for supporters to monitor polling places in “certain areas.”

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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 Ohio lawsuit states. “Trump’s exhortations have grown more ominous and specific as the election draws closer.”

The lawsuits in all four states, which included similar allegations, cited a Bloomberg Businessweek report that quoted an anonymous Trump official as saying that the campaign had “three major voter suppression operations underway.” In the report, the official said the campaign was seeking to drive down turnout among African American voters.

In North Carolina, another key venue on Election Day, the state NAACP filed a federal lawsuit Monday saying that three counties — Beaufort, Moore and Cumberland — had improperly canceled the registrations of thousands of voters. The state election board said that private citizens, rather than any county officials, had challenged the registrations.