Writer Owen, 32, clashed heavily with Piers, 51, as they discussed whether the controversial Commander-in-Chief should be granted a state visit by Britain.
However, Owen refused to be talked over by the Good Morning Britain presenter, who is known to interrupt guests and even co-host Susanna Reid.
“This is a monologue, this isn’t an interview!” Owen was heard telling Piers, before suggesting that the pair had a monologue-off as the two men sparred.
As Owen tried to speak, Piers continued, leading the former to exclaim: “The production staff are laughing at you!”
When Owen was finally allowed to speak, he told the hosts that Prime Minister Theresa May had “failed” Britain by not standing up and denouncing Trump’s controversial travel ban.
“We don’t want to become a client state for Donald Trump,” he said, adding that he thought the premier should “stand up” to the president.
Piers responded, saying: “Year after year we have rolled out the red carpet. Where were the mass marches? Why didn’t you turn out?”
Owen Jones and Piers Morgan clash on Good Morning Britain
Owen Jones hit back at Piers Morgan on Good Morning Britain
This is a monologue, this isn’t an interview!
He named the leaders of China and Saudi Arabia as previous controversial countries who have been given state visits despite their poor record on human rights in their own nations.
Owen said that he had in fact led the march against the state visit by the leader of Saudi Arabia in the past and had protested outside the embassy in London.
But Piers didn't back down, saying: “I think there’s a hypocrisy over our state visit. You can’t single out one leader. I get he’s a very divisive character but he was the victor in a free, democratic election.”
Owen Jones also clashed with MP Philip Davies on Good Morning Britain
He continued: “You were absolutely incandescent and marched and protested. I’ve got nothing wrong with you protesting but I am not sure it makes any difference. I think the hysteria of the left is empowering him.”
Owen called on the government to show their opposition to the travel ban but Piers refused to back down, saying: “There weren’t the mass protests [for other leaders]. We have to be fair-minded about that. You don’t like Trump. There is a vitriolic hatred of him.”
He continued, saying that Britain needed the US as an ally and questioned if Owen wanted the British PM to “make her Hugh Grant Love Actually speech”.
Piers’ comments led Owen to respond that the fictional PM had shown greater leadership than Mrs May, before saying that she was “disappearing up the backside of the US government” and had “held hands with him”.
Owen Jones and Piers Morgan debate Donald Trump on Good Morning Britain
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Owen Jones hits back at Piers Morgan on Good Morning Britain
It was then that Piers interrupted him and addressed the hand holding, causing Owen to say: “I can’t answer because you keep yelling. Germany have offered leadership. We look weak because you’ve failed to stand up for our [values].
"This is the most powerful country on earth, Americans said we are legitimising [the ban].”
In an exasperated voice, Owen added: “I need an aspirin.” Piers hit back: “I need a cold shower, we’ve all got a cross to bear.”
The latest clash follows on from one between Piers and Shami Chakrabarti on the ITV show yesterday.
Good Morning Britain airs weekdays on ITV at 6am.