The chairman, Michael McDonald, was referring to a polling location in Clark County, which is 30% Hispanic and the county in which Las Vegas is located. The polling location stayed open to allow voters who were already in line -- many of whom waited more than two hours, according to local reports -- to cast their ballots.
"Last night, in Clark County, they kept a poll open 'til 10 o'clock at night so a certain group could vote," McDonald said in introductory remarks at the rally. "The polls are supposed to close at 7. This was kept open until 10. Yeah, you feel free right now? You think this is a free and easy election? That's why it's important."
Dan Kulin, a spokesperson for the county, said no early no early voting stations extended their closing times. They did, however, process voters who were in line at closing time to allow as many people to vote as possible.
The latest vote was cast at 10:10 p.m. at Silverado Ranch, which closed at 8 p.m. and had been experiencing about a two-hour delay when CNN visited the station.
A message left with the Trump campaign was not immediately returned.
Taking the stage here, Trump then suggested that the polling location's extended closing time to allow voters to cast their ballots is a sign of a "rigged system" pitted against his campaign.
"It's being reported that certain key Democratic polling locations in Clark County were kept open for hours and hours beyond closing time to bus and bring democratic voters in. Folks, it's a rigged system. It's a rigged system and we're going to beat it. We're going to beat it," Trump said Saturday.
His remarks were delivered before someone in the audience shouted "gun," leading Secret Service agents to escort him off the stage. Trump was unharmed in the incident, and the Secret Service said in a statement that after a "thorough search," no weapon was found.
Polling locations are non-partisan, and a spokesperson with Clark County said voters who were already in line before the polls closed were still allowed to vote -- a common practice at polling locations around the country.
More than 57,000 people voted in Clark County on Friday, the largest single-day early voting turnout in the county, according to data
from the Nevada secretary of state's office that's based on the party registration of those who have voted.
While polls are showing Trump competitive in the state, a surge of Hispanics casting their votes in early voting in the state has led many political observers to believe Trump's path to victory in the state has significantly narrowed.