He told a rally in Columbus, Ohio, that he had heard “more and more” that the contest would be unfair. He offered no immediate evidence.
At another event he called Democratic rival Hillary Clinton “the devil”.
Mr Trump has come under fire from across the political divide for remarks he made about the parents of a US Muslim soldier killed in action.
On the forthcoming vote, he told supporters “I’m afraid the election is going to be rigged, I have to be honest”.
He later repeated the claim on Fox News, adding “I hope the Republicans are watching closely or it’s going to be taken away from us.”
Mr Trump has made similar comments before in relation to the Democratic race, suggesting the party fixed its system to favour nominee Hillary Clinton over her challenger Bernie Sanders.
Earlier this year, he also complained the Republican primary system was also “rigged” amid party efforts to stop his march to the candidacy.
Correspondents say Mr Trump could be trying to capitalise on voters’ distrust of establishment institutions, or lay the groundwork should he lose the election.
At another rally in Pennsylvania, he took the unprecedented step of directly calling Mrs Clinton “the devil”.
He attacked Mr Sanders for capitulating in the Democratic race, saying he “made a deal with the devil. She’s the devil.”
Democrats and Republicans alike have condemned Mr Trump for his remarks about the parents of US Army Capt Humayun Khan, who was killed by a car bomb in 2004 in Iraq, at the age of 27.
Former Republican presidential candidate John McCain became the latest senior figure in the party to criticise Mr Trump for his attacks.
Senator McCain, a veteran of the Vietnam War, said in a strongly worded statement that Mr Trump did not have “unfettered licence to defame the best among us”.
The soldier’s parents, Khizr Khan and his wife Ghazala, told the BBC it was time to stand up to Mr Trump but he accused them of “viciously” attacking him.
Mr Trump had caused controversy by suggesting Ghazala Khan had been prevented from speaking alongside her husband at the Democratic convention last week.
In another development, American billionaire businessman Warren Buffett challenged Mr Trump to release his tax returns.
Mr Trump has said that they cannot be made public until the financial authorities have completed an audit.
But Mr Buffett said there were no rules against showing tax returns and allowing people to ask questions about them.