The delay was caused by a relatively slow vote count across several swing states – specifically Pennsylvania, Michigan, Wisconsin, Georgia, North Carolina, Arizona and Nevada.
A month after the election, Trump and his legal team have yet to provide any evidence to support their claims that widespread fraud robbed him of victory.
The President and his allies have suffered dozens of defeats in court. Judges have repeatedly labelled their claims not credible, without merit or unsupported by proof.
"We used to have what we called election day. Now we have election weeks and months. And lots of bad things happened during this period of time," Trump said in the pre-recorded speech.
"Especially when you have to prove almost nothing to exercise our greatest privilege, the right to vote.
"As President I have no higher duty than to defend the laws and the Constitution of the United States. That is why I am determined to protect our election system, which is now under co-ordinated assault and siege.
"For months leading up to the election, we were warned that we should not declare a premature victory. We were told repeatedly that it would take weeks, if not months, to determine the winner, to count the absentee ballots, and to verify the results."
No one said it would take months to determine a winner. The warning from election experts, covered extensively in the news media, was that a surge in mail voting due to the coronavirus pandemic meant there might not be a clear result on election night.
The experts said Trump and Biden would each appear to be well ahead in certain states, depending whether or not the state in question counted mail-in ballots (which are overwhelmingly Democratic) ahead of time.
They said these early leads would prove to be a "mirage" – a blue one in some states and a red one in others.
This happened as forecast across much of the country. In states such as Florida and North Carolina, which allowed election officials to count the mail vote before election day, Biden leaped to early leads. Trump won both states.
In Pennsylvania, Michigan, Wisconsin and Georgia, where officials had to wait until election day to start, Trump led by large margins early and Biden eventually reeled him in.
The President declared victory on election night, before most of the mail-in votes across those states had been counted, despite the experts' warnings. Ever since, he has argued that Biden's comeback was suspicious and tainted by massive fraud.
He has also taken to arguing that Biden has claimed victory prematurely.
"It was all very, very strange. Within days after the election, we witnessed an orchestrated effort to annoint a winner even while many key states were still being counted," Mr Trump continued.
"We are going to ensure the honesty of the vote by ensuring that every legal ballot is counted, and that not illegal ballot is counted.
"This is not just about honouring the votes of 74 million Americans who voted for me. It is about ensuring that Americans have have faith in this election and in future elections."
He went on to claim the campaign "already has the evidence" it needs to prove its assertions about fraud.
"This election was rigged. Everybody knows it," said Trump.
"I don't mind if I lose an election. But I want to lose an election fair and square. What I don't want to do is have it stolen from the American people.
"That's what we're fighting for, and we have no choice (but) to be doing that. We already have the proof, we already have the evidence, and it's very clear.
"Many people in the media, and even judges so far, have refused to accept it. They know it's true, they know it's there, they know who won the election. But they refuse to say, 'You're right.' Our country needs somebody to say, 'You're right.'"
The fundamental problem here is the dramatic disconnect between Trump's claims in public and his lawyers' claims in court, where they have not alleged a single specific instance of voter fraud.
In Pennsylvania earlier, the Trump campaign tried to stop the state from certifying its results.
The head of Trump's legal team, Rudy Giuliani, argued that case himself. Under questioning from Judge Matthew Brann, he conceded it was "not a fraud case".
Rather, the campaign has argued a patchwork of legal technicalities in an attempt to disqualify votes that favoured Biden. For example, in that Pennsylvania case, it said 680,000 ballots from Philadelphia should be thrown out because Republican poll watchers were blocked from properly observing as they were counted.
Incidentally, the Pennsylvania Supreme Court has rejected that claim, saying election officials' treatment of observers was lawful.
The closest the campaign has come to presenting proof of actual fraud was in the form of affidavits signed by some of its observers.
Giuliani often says he has hundreds of these affidavits, though only a handful have actually been filed in court. Thus far, they have failed to impress any of the judges.
For example, Judge Timothy Kenny ruled that about half a dozen affidavits from Republican poll watchers in Michigan were "incorrect and not credible", saying the people in question did not "have a full understanding" of the vote-counting process.
That is polite judge-speak for saying they had no idea what they were talking about. You can read Judge Kenny's full decision here.
A judge in Arizona berated Trump's lawyers over the affidavits they had submitted to him, noting they had solicited testimony from witnesses without checking whether it was actually reliable.
Trump and Giuliani have been saying for weeks that they already have convincing, incontrovertible evidence. All this time later, none of that proof has shown up in a courtroom.
In other words, the President is accusing judges - some of whom he appointed himself - of "refusing to accept" evidence his lawyers have not even presented.
MORE TO COME
