The Oscar-winning documentary maker, who in July accurately predicted Mr Trump would win, argued a re-election was needed because the President did not win the popular vote.
Mr Trump gained nearly three million fewer votes than his Democrat rival Hillary Clinton. The margin of 2.86 million ballots was the biggest popular vote disparity in US history for a candidate who has gone on to become President, significantly greater than the 544,000-vote gap between George W Bush and Al Gore in 2000.
Moore agreed with a New York Times story claiming members of Mr Trump’s presidential campaign team had multiple interactions with senior Russian officials in the year before the election. The President has dismissed unconfirmed allegations over Russia as "conspiracy theories" fed to the media by intelligence agencies.
But Moore, who has emerged as a leading critic of the President, went a step further than the piece.
“It's what we all suspected. It doesn't take a rocket scientist to figure out what was going on: Trump colluding with the Russians to throw the election to him,” he said in a scathing Facebook post.
Moore then outlined a four point plan to move forward, which starts with calling for the billionaire property mogul to be impeached.
“I and tens of millions of Americans demand that the weak and spineless Democrats bring Congress to a halt until investigative hearings are held and impeachment charges are filed,” he said.
The filmmaker followed this up by calling for Attorney General J Beauregard Sessions to immediately appoint a Special Prosecutor to investigate these “potentially treasonous acts”.
“So-Called President Trump could save the country a lot of time, money and pain by stepping down tonight,” he said.
But Moore was insistent Mr Trump should not under any circumstance be replaced by Vice President Mike Pence. Instead the documentary-maker, who has enjoyed a renaissance since Mr Trump declared his presidential bid, argued Republicans should not be able to hold on to power “by default”.
“Somehow, our judicial system has to find a way to make restitution to this country. Pence can't be president as he, too, was elected under this same fraud,” Moore said. “The court has to rule either that the President is the winner of the popular vote OR the election must be held over. The Republicans - the beneficiaries of this treason - cannot be allowed to hold on to the power by default. If it turns out there's a traitor in the White House, the judicial branch must find a fair, peaceful way to un-do and then re-do the election of 2016.”
Moore previously positioned himself as a Bernie Sanders supporter, but after the news that Mr Sanders had dropped out, he announced he would vote for Ms Clinton in order to keep Mr Trump out the White House. He has called on Americans to transform their anger at Mr Trump’s victory into action via protests and civil disobedience.
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