The mob's outrage had apparently been sparked by the number plate of the Porsche Clarkson had been given to drive in the country, which read H982 FKL.
It is thought the locals assumed the lettering to be a sly reference to the 1982 war between Argentina and the UK over the Falkland's.
However, Clarkson tweeted that the entire incident had been down to unfortunate coincidence.
"This was not a jolly jape that went awry," he wrote. "For once, we did nothing wrong. We had planned a good ending to the show. But thanks to the government's foolishness, it's now even better.
"They threw us out for political capital. Thousands chased crew to border. Someone could have been killed.
"My profound thanks to all the people who helped. And to the sensible Argentinians who have apologised."
The show's producers have since reiterated their claims that the number plate was not a deliberate jibe.
They confirmed, however, that it did spark a number of demonstrations, including one from supposed war veterans who protested outside the hotel the Top Gear crew had been staying in.
"Top Gear production purchased three cars for a forthcoming programme; to suggest that this car was either chosen for its number plate, or that an alternative number plate was substituted for the original, is completely untrue," Top Gear's executive producer, Andy Wilman, said.
The show has come under heavy criticism in the part for a number of perceived racial insensitivities.
There was a public backlash against Clarkson earlier this year when it emerged that he had used the n-word in nursery rhyme "Eeny, Meeny, Miny, Moe" during a Top Gear outtake.
The show was investigated after the presenter called an Asian man a "slope" as part of a "humorous" play on words during the Burma special in 2013.
Clarkson has also been criticised for jokes about Mexicans and other national groups in the past.
- Independent