Trump kept his answers short, taking shots at Acosta several times before moving to end the questioning.
A frame-by-frame comparison of the video shows that Sander's clip has been edited to speed up Acosta's arm movement as he touches the woman's arm.
Sanders has not confirmed the source of the video she tweeted.
During the heated exchange, the US President accused the CNN reporter of being the "enemy of the people". "She provided fraudulent accusations and cited an incident that never happened", CNN added in its statement.
"I think Jim Acosta is a very unprofessional man-he does this with everybody".
The episode will reignite fears that Mr Trump has scant regard for press freedom and is intent on limiting space for critical coverage.
He begins by questioning him on his comments about the "migrant caravan" Trump has claimed is heading for the U.S. before turning to Russian Federation.
After a few moments of verbal sparring, Trump angrily declared "that's enough" as a White House aide moved to take the microphone away from Acosta. "You shouldn't be working for CNN". You are a rude, awful person.
"You talk about somebody that's a loser, she doesn't know what the hell she's doing", Trump said.
That's when Trump said, "CNN should be ashamed of itself having you working for them".
I'd say "willingness to mislead" is the functional equivalent of a lie. You are not the best.