"In June of 1775, the Continental Congress created a unified Army out of the Revolutionary Forces encamped around Boston and New York, and named after the great George Washington, commander in chief," Trump said during his "Salute to America" speech at the Lincoln Memorial on Thursday - although the Army was not named after Washington.
"Our Army manned the air, it rammed the ramparts, it took over the airports, it did everything it had to do, and at Fort McHenry, under the rocket's red glare it had nothing but victory," he added.
But observers quickly pointed out there was no air travel in 18th Century America. They said the rebels could not have seized airports more than a century before the first powered flight - credited to the Wright brothers in 1903 - took off.
In the same sentence, Trump also appeared to date a battle at Fort McHenry to the American Revolution, when it unfolded decades later during the War of 1812.
Explaining the slip-up on Friday, Trump said it was hard to read the teleprompter in the rain, the US media reported.
"We had a lot of rain. I stood in the rain. The teleprompter went out," he told reporters outside the White House. "It kept going on, and then at the end, it just went out. It went kaput!"
He said the moment of technical failure came when he made the widely derided remark about eighteenth-century airports.
Without apologizing for the mistake, Trump said it wasn't pleasant to see the scrolling stop as he was delivering his highly anticipated speech.
"That's not a good feeling when you're standing in front of millions and millions of people," he said. "I guess the rain knocked out the teleprompter."
Still, he said his memory of the speech otherwise served him well. "I knew the speech very well so I was able to do it without a teleprompter," he said. "And it was actually hard to look at anyway because of the rain."
On several previous occasions, Trump derided critics for relying on a teleprompter when delivering speeches.
In 2012, he said of then-President Barack Obama, "Why does @BarackObama always have to rely on teleprompters?"
In 2016, he railed on his Democratic opponent Hillary Clinton tweeting: "Bad performance by Crooked Hillary Clinton! Reading poorly from the telepromter! She doesn't even look presidential!"
( With inputs from IANS )