The ex-Mirror editor blasted Robinson, 34, for “stirring up hatred” in an appearance on the ITV breakfast programme on Tuesday morning.
As Robinson waved a copy of the Koran, an angry Morgan said: “Show some damn respect for people’s religious beliefs.
“You’re sounding like a complete lunatic. You’re sounding like a bigoted lunatic.
“You’re stirring up hatred.
“You’re being a complete disgrace.”
But Robinson spat back: “We’re in this mess because people take Islam, they are terrorists and they abuse the nature of Islam and [they] perpetrate evil.”
He added: “There’s no such word as Islamophobia. A phobia is an irrational fear, it’s not irrational to fear these things.”
You’re being a complete disgracePiers Morgan to Tommy Robinson
He went on to suggest Piers took issue with him because of his “accent”, to which the presenter hit back: “Don’t play the class card with me.”
“You’ve repeated what I’ve said for 10 years speaking better English,” Robinson said.
Robinson’s invitation onto the ‘GMB’ sofa provoked fury from some on Monday, with people arguing he should not be given air time.
Robinson tweeted after his appearance: “I hope my passion didn’t come across as anger.”
After founding the EDL, his relationship with the group soured when he joined anti-extremist think tank Quilliam in 2013. Despite the brief interlude, he later became coordinator for anti-Islam group Pegida UK.