His comments appear to contradict his running mate Mike Pence, who told NBC Mr Trump would "absolutely" accept the election result, despite media "bias".
Mr Trump's adviser Rudy Giuliani has also accused Democrats of "cheating".
Polls suggest Mr Trump is losing ground in some key battleground states against Democratic rival Hillary Clinton.
Mr Trump has questioned the legitimacy of the election process in a series of tweets, the latest of which said on Monday: "Of course there is large scale voter fraud happening on and before election day.
"Why do Republican leaders deny what is going on? So naive!"
An earlier tweet said: "The election is absolutely being rigged by the dishonest and distorted media pushing Crooked Hillary - but also at many polling places - SAD."
The White House candidate also tweeted: "Election is being rigged by the media, in a coordinated effort with the Clinton campaign, by putting stories that never happened into news!"
Speaking on NBC's Meet The Press on Sunday, Republican vice-presidential candidate Mr Pence said Americans were "tired of the obvious bias in the national media".
But he added: "We will absolutely accept the results of the election."
"Elections always get pretty rough," he added, but said the US has a tradition of "the peaceful transfer of power".
Former New York Mayor Rudy Giuliani, who is Mr Trump's campaign adviser, told CNN's State of the Union he'd have to be a "moron" to think that some elections, such as those in Philadelphia and Chicago, were going to be fair.
"I've found very few situations where Republicans cheat... they don't control the inner cities the way Democrats do. Maybe if Republicans controlled the inner cities, they'd do as much cheating as Democrats," he said.
"I'm sorry. Dead people generally vote for Democrats rather than Republicans," he added.
Donald Trump has claimed for months that the election was rigged - but that message is now at the centre of his campaign just as his poll numbers begin to slump. And in doing so he hits at the very heart of American democracy - the idea that elections are free and fair.
Mr Trump's tactics allow him once more to paint himself as the anti-establishment figure being victimised by the Washington political elite. It also gives him an excuse if he loses.
But where would it leave his supporters?  The fear is that the Republican candidate's rhetoric could further divide this country and stoke anger and suspicion among the millions who follow him.
If Hillary Clinton is elected, would they accept her presidency as legitimate and if not, what form would those protests take?
Mrs Clinton's running mate Tim Kaine blasted Mr Trump's election-rigging claims as "scare tactics".
He told ABC's This Week Mr Trump was "swinging at every phantom of his own imagination" because "he knows he's losing".
Multiple women have come forward to accuse Mr Trump of groping or kissing them in the past week, following the emergence of a 2005 video tape in which the Republican nominee made obscene remarks about women.
He has repeatedly denied the claims, calling the women "horrible liars" and accusing the media of being an agent of the "Clinton machine".
Mr Kaine denied that the Clinton campaign had anything to do with the women making accusations against Mr Trump.
Who is ahead in the polls?
48%
Hillary Clinton
44%
Donald Trump
Last updated November 8, 2016
US Republican presidential nominee Donald Trump has said the election is "absolutely rigged" by the "dishonest media" and "at many polling places".