Mr Pritzker, a Democrat, called in to CNN’s OutFront, hosted by Erin Burnett, to criticise the president for saying that he is “your president of law and order” on Monday.
Mr Trump made the remarks after he ordered police to disperse a group of protesters with tear gas and rubber bullets, when he left the White House yesterday to visit a nearby church for a photo opportunity.
The Illinois governor told Ms Burnett: “The fact is that the president has created an incendiary moment here,” with his handling of the protests.
“He wants to change the subject from his failure over coronavirus, a miserable failure.
“And now seeing a moment when there’s unrest because of the injustice that was done to George Floyd that he now wants to create another topic and something where he can be the law and order president. He’s been a miserable failure,” the governor added.
Protests began last week, when Mr Floyd died after then Minneapolis police officer, Derek Chauvin, knelt on his neck while detaining him. Mr Chauvin has since been charged with third-degree murder and manslaughter.
The protests, which are being held in opposition to police brutality against Black Americans, following Mr Floyd’s death, initially started in Minneapolis last week, but spread to Chicago and New York, among other cities in the US over the weekend.
Police have clashed with protesters all over the US, and on Monday, Mr Trump said that he would bring in the military to stop protests if he feels that he needs to.
“We are ending the riots and lawlessness that has spread across our country. We will end it now,” he said.
“If a city or state refuses to take the actions that are necessary to defend the life and property of their residents, then I will deploy the United States military and quickly solve the problem for them.”
Mr Pritzker confronted the president about his response to the protests, during a video call on Monday, the audio of which was obtained by CNN.
During the phone call, Mr Pritzker said that “rhetoric coming out of the White House is making it worse, people are experiencing real pain”, and added: “We’ve got to have national leadership calling for calm and legitimate concern for protesters.”
Mr Trump replied to the governor and said: “I don’t like your rhetoric that much either,” and added “You could have done much better on coronavirus”.
Speaking to Ms Burnett after the call, the governor said that the president’s rhetoric during the protests has been bad for the US, and added that he does not think Mr Trump understands the job of president.
“It’s clear that he doesn’t listen to anyone that tells him the truth. I did tell him the truth. You know, this rhetoric, this inflammatory rhetoric is bad for the country,” he said.
“You know, when we had the riots in Ferguson, President Obama started to bring the temperature down. He talked about calling for calm. When, you know, when Martin Luther King was killed, Robert Kennedy stood up and talked about seeking justice, you know, and bringing the tension down within the country.”
Mr Pritzker added: “This President doesn’t understand any of that.
“He probably hasn’t read any of that, knows no history, and doesn’t understand the job of the president to truly speak to the values of the nation.”
The Independent has asked the White House for comment.