Thousands of demonstrators across the US ignored curfew and took to the streets for an eighth consecutive night, while London protesters will gather in Hyde Park this afternoon.
Mr Trump has threatened to deploy to the military to quell the civil unrest, which has seen some outbreaks of violence and looting in cities, although last night’s demonstrations were largely peaceful.
He said: "Imagine if Donald Trump, rather than stirring the fire and pouring fuel on it, imagine if he came out of the White House with those protesters and went down on one knee.
"Imagine the power of Donald Trump doing that, and what impact that might have.”
The idea of “taking the knee” in protest against racial injustice was inspired by NFL player Colin Kaepernick, who faced a backlash from the American right for refusing to stand during the national anthem before games.
In recent days, a number of US police officers have imitated the the move to express solidarity and understanding with those protesting.
Mr Morgan added: "In one action, I genuinely believe [Trump] could make an enormous difference.
"I don't think he has it in him, I don't think he thinks it could win him an election, but I think morally it would be the right thing to do."
The presenter and his co-host Susanna Reid were speaking with Martin Luther King III, the eldest son of Martin Luther King Jr., via videolink from Georgia.
The human rights advocate agreed with Morgan, adding: "There is no question about that.”
Against the backdrop of social hardship caused by the coronavirus pandemic, Mr Floyd’s death on May 25 in Minneapolis sparked off the most serious wave of civil unrest in the US since 1968.
The 46-year-old African American died after a white police officer in Minneapolis knelt on his neck for almost nine minutes to restrain him. Footage of Mr Floyd gasping “I can’t breathe” before losing consciousness sparked outrage around the worldwide.
Once one of the President’s staunchest supporters in the UK media, in recent months Morgan has strongly criticised Mr Trumps’ handling of the coronavirus crisis.
At one point the GMB presenter who was 7.5 million Twitter followers, was only one of 40 people that the President — an avid tweeter — followed on the platform.
But that apparent mutual admiration came to an abrupt end in April after the presenter described Trump's theory about injecting disinfectant to cure Covid-19 as "bat****”.