The tweet, likely supposed to be scheduled for last Tuesday, was deleted less than an hour after it was posted, but not before drawing ridicule online.
One user mockingly lamented: “When you schedule the tweet but it’s already after dad lost the election.”
Pennsylvania state representative Brian Sims replied: “BLURP: So the ‘team’ that scheduled a press conference at a landscaping business, and a tweet a week after the election, wants you to believe they’ve discovered fraud somewhere.”
Another tweet quipped: “Tired: We must know the winner on election day! Wired: We must continue voting a week after the election!”
The same user followed up with: “Hey, Eric. What's the number for that voter fraud hotline? I need to report something.”
Writer Tony Posnanski posted: “Dammit! I guess Eric is the dumbest Trump child today.”
A gif of Eric Trump as portrayed by Alex Moffat on Saturday Night Live, showing the executive vice president of the Trump Organisation drinking hand sanitiser, was also posted a number of times.
The younger Mr Trump has been recently mocked online for tweeting false claims about ballots being burned; about big tech "censoring" his posts that get less likes; and for complaining that Democrats were flooding the Trump campaign voter fraud hotline with spam messages.
Democratic candidate Joe Biden won the state of Minnesota in the 3 November election with 52.6 per cent of the vote.
On Saturday, Mr Biden was named president-elect after the Associated Press and a number of other media organisations called the election in his favour, having accrued 290 electoral college votes.
Donald Trump and his family are yet to acknowledge the loss.
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