Campaigning in Joe Biden’s hometown of Scranton, Pennsylvania, Mr Trump told Tom Wolf, the Democrat governor, that he was paying close attention.
“You look at what’s going on in Philadelphia – we’re watching you, governor,” he said.
“Make sure your governor doesn’t cheat, because they are known for very bad things here.
“But we have a lot of eyes watching, a lot of very powerful eyes here.
“They don’t want that to happen.”
It was not immediately clear exactly what the president was referring to, although he may have been alluding to what his campaign claimed was evidence of voter fraud at polling stations last month, allegations that were denied.
Philadelphia has also been gripped by violence and in recent days following the shooting dead of a Black man, Walter Wallace, by police.
The White House said that the riots were the result of the “Liberal Democrats’ war on law enforcement”.
Over 100 people were arrested and at least 30 police officers injured in several nights of violence, but Mr Wolf said that the demonstrations had been largely peaceful — a statement mocked by Republicans.
Pennsylvania is seen by analysts as a vital state for both Mr Trump and Mr Biden, and currently hangs in the balance.
Both candidates have been campaigning hard in the state: Mr Trump held four rallies there on Saturday, while Mr Biden dispatched his “star player”, Barack Obama, last week to kick off his in-person campaigning.
Mr Trump won the state four years ago, but Mr Biden is ahead by five points among likely voters, 51 per cent to 46 per cent — although that advantage is within that poll’s margin of error.
A combined three per cent say they are undecided, or are voting for someone else.
“At every turn, Biden twisted the knife into the back of Pennsylvania workers,” Mr Trump said in Montoursville on Saturday, in his ninth rally in the state since recovering from Covid-19.
“They keep saying it’s close [in Pennsylvania] but I don’t think it’s close.”
His Democratic rival and Kamala Harris, Mr Biden’s running mate, spent the day fanning across the state in a final pitch to voters.
Mr Trump’s “warning” to Mr Wolf came amid very real fears of violence marring the election, and his comments will not be welcomed by those seeking a calm and peaceful electoral week.
Supporters of the president, in self-made “militias”, have already confirmed that they will be “monitoring” the polls in various states.
Many fear that the presence of heavily-armed men and women around polling stations borders on voter intimidation, and could provoke an equally-strong counterprotest.
On Friday ugly scenes erupted in Texas, forcing the cancellation of Biden’s team’s planned activities.
A bus was driving on Interstate 35 between Laredo and San Antonio, with Texas congressional candidate and former state senator Wendy Davis on board, when it was surrounded by nearly 100 trucks decked out in Trump campaign gear.
Eric Cervini, a Biden campaign volunteer who joined the bus tour in his home state to help “drum up enthusiasm” before Tuesday’s vote, said he spent the afternoon calling 911 as the caravan confronted the bus between San Antonio and Austin.
“These Trump supporters, many of whom were armed, surrounded the bus on the interstate and attempted to drive it off the road,” he said in a series of tweets recounting his experiences.
“They outnumbered police 50-1, and they ended up hitting a staffer’s car.”
People traveling with the campaign bus called 911, and police from New Braunfels, a town along their route on I-35, responded and provided a police escort.
Police “responded and did not observe any traffic violations,” the New Braunfels city manager told the Texas Tribune, and Mr Trump has praised their actions.