The radio show host, who classifies himself as a libertarian, appeared as a guest on the interview programme to discuss his petition to get Piers Morgan deported from the United States.
During a heated debate with Morgan about gun control, Jones said: "The megabanks that control the planet and brag that they've taken over and Bloomberg, AP, Reuters, you name it, brag that they're going to get our guns as well.
"They've taken everybody's guns but the Swiss and the American people, and when they get our guns they can have world tyranny."
Jones has now taken to YouTube in the wake of the debate to claim that undercover cops are following him, calling New York City Mayor Michael Bloomberg "total mafia".
Jones explained: "The way this'll work is, 'Oh, see here they were protesting gun grabs and some crack dealers shot them'. If something happens to us, we're killed by crackheads, it was the NYPD or the mafia they hired."
He added: "This city runs white slaves, that's sex slaves, out of here all day. This is mafia central."
The White House has since issued an official response to Jones's petition, which currently has over 100,000 signatures.
A spokesperson said in a statement that "the White House responds to all petitions that cross the [25,000-signature] threshold and we will respond to this one.
"In the meantime, it is worth remembering that the freedom of expression is a bedrock principle in our democracy."
Watch Alex Jones's video message below: