While many of the demonstrations around the country have been peaceful protests by racially diverse crowds, others have descended into violence, with riot police and thousands of National Guard troops deployed in at least 15 states.
The nationwide protests were sparked by the death of Mr Floyd, an unarmed black man in Minnesota and were ignited again on Monday night after Trump emerged after two days out of public view and threatened to deploy “thousands and thousands” of troops.
A white police officer has been charged with third-degree murder and second-degree manslaughter following Mr Floyd's death.
America's capital has become the new epicentre of these protests as demonstrators' anger is increasingly directed at President Donald Trump who remains defiant in the face of rising fury.
Mr Trump has called the "violent" protests "acts of domestic terror" and has threatened to put troops on the streets.
On Monday night, law enforcement officers fired tear gas, deployed flash bangs and shot rubber bullets into the crowd protesting peacefully in a park in order to clear the way for Mr Trump to walk to a nearby church for a photo opportunity.
The president declared he would be putting more guards on the streets of the capital although it is not clear if he has the constitutional right to do that.
On Friday night, Mr Trump was forced to take shelter in the White House's bunker as protests reached the gates.
Marc Lotter director of strategic communications for Mr Trump’s 2020 re-election campaign defended the president's actions, telling BBC Radio 4's Today programme: "It was absolutely the appropriate act of the United States Secret Service and the police to create a perimeter around the White House to make sure that there’s security, that we’re not having our national historic sites set on fire.”
Senator for Florida Marco Rubio also backed the president calling the protestors “professional agitators”.
“They knew the street needed to be cleared before 7 pm curfew,” Rubio tweeted. “But they deliberately stayed to trigger police action & get the story they wanted, that “police attacked peaceful protesters.”
Following a weekend of protests, which led to looting and vandalism by a minority, curfews have been put in place across Los Angeles - as early as 1pm in some areas.
Nearly 1,000 people have been arrested in the city, while elsewhere in the state, protests spilled over into violence.
Shops were vandalised, police cars torched and many officers injured as unrest escalated; in Sacramento, alone, two-thirds of downtown businesses were damaged
There are now 500 National Guards deployed, and the city has declared an 8pm curfew on Monday.
On Monday, demonstrations across the state remained peaceful, with protesters largely dispersing as curfews took effect.
But after dark, smaller, rowdier groups tossed fireworks and bottles at police and sheriff’s deputies in several cities. Tear gas and rubber bullets were used to disperse people in Oakland and elsewhere.
Most protests also were smaller, although an estimated 15,000 people gathered in Oakland and about 5,000 in Riverside, east of Los Angeles.
In San Diego, a police car was seen driving into a crowd of protesters in footage captured amid unrest on Sunday.
The video shows demonstrators blocking the path of a police car before it lurches forward into the crowd.
The vehicle continues to advance, dragging a protester along with it on its hood, while people scream in the background.
At the spot where George Floyd died, hundreds of flowers and messages of condolences have been left by mourners at a makeshift memorial.
Protests in his home state in the wake of Mr Floyd's death were mostly peaceful, but there were pockets of violence that led to a considerably ramped up law enforcement response.
Hours later, video emerged of police shooting paint projectiles at people gathered on the front porch of a home after curfew in Minneapolis.
But demonstrations had died down by the end of the weekend; on Monday Mr Floyd's brother Terrance visited the memorial and called for calm.
“I understand you all are upset ... (but) if I’m not over here blowing up stuff, if I'm not over here messing up my community, what are y’all doing?” he said to the crowd.
“That’s not going to bring my brother back at all.”
An officer was shot near the Circus Circus casino on Monday, while another police officer was involved in a shooting in the city's downtown area, according to the Las Vegas Metropolitan Police Department.
Police said 338 people were arrested in Vegas over three nights of protests.
Las Vegas police said riot officers did not use rubber bullets on protestors instead holding demonstrators back with non-lethal projectiles similar to paint balls but containing an irritant powder.
Most of the protests in New York have been peaceful marches but as night fell, there have been increasing instances of looting and vandalism.
Arrests were made inside the iconic Macy’s store in Manhattan amid violence on Monday following looting and vandalism and people ransacked luxury stores in Manhattan’s chic Soho neighbourhood.
Meanwhile, video showed two police vehicles driving into a crowd, knocking aside demonstrators.
Law enforcement officers killed an unarmed black man while trying to disperse crowd in Louisville, Kentucky.
David McAtee, a BBQ chef who was described as a "pillar in the community", died after Louisville police and members of the National Guard opened fire on a crowd.
Reports on Twitter say Mr McAtee used to hand out free food to police officers on duty.
Authorities say they acted in defence after someone in the crowd fired the first shot but first hand witnesses have disputed the police’s account of events.
People gathered on the street to silently mourn Mr McAtee on Monday. People took to the streets to peacefully protest his death, with many standing, arms raised in the Black Power salute as a woman sang.
Thousands of people gathered in downtown Seattle in the rain on Sunday following a largely peaceful demonstration on Saturday afternoon that turned more violent as night fell.
Police deployed flash bangs to disperse people they said had begun throw rocks and bottles at officers. Police also pepper-sprayed demonstrators who got close to police lines, and officers with bicycles pushed people to move back.
A 5pm curfew was declared and although many dispersed soon after, dozens remained in defiance of the curfew, setting fires, breaking into retail stores and taking items while police fired tear gas and arrested at least one person.
Voices from across the United States
High profile African Americans have been adding their voices to the chorus of support for the protests.
On Sunday, basketball legend Michael Jordan released a statement saying he stood "with those who are calling out the ingrained racism and violence toward people of colour in our country. We have had enough."
"I don't have the answers, but our collective voices show strength and the inability to be divided by others.
"We must listen to each other, show compassion and empathy, and never turn our backs on senseless brutality. We need to continue peaceful expressions against injustice and demand accountability. Our unified voice needs to put pressure on our leaders to change our laws, or else we need to use our vote to create systemic change."
Singer John Legend, a frequent critic of the president, accused Mr Trump of using law enforcement to clear peaceful protesters so he could get a photograph.
He tweeted: “#BunkerBoy Trump had to prove he could walk in broad daylight today so he sicced the police on peaceful protesters so he could stand there and awkwardly hold the Bible. Dear God. We need to end this nightmare of a presidency.”
Oscar-winning filmmaker Spike Lee, who refers to Mr Trump as “Agent Orange”, wrote on Instagram that the US was on the verge of a dictatorship.
Grammy-winning rapper Cardi B accused the president of threatening people and making protesters “more angry”.
Samuel L Jackson suggested Mr Trump had “declared war on the public."
Following Mr Trump’s press conference, One Direction star Niall Horan, who earlier accused the president of “hiding”, wrote: “Can’t believe what I just watched.”
But there are many in America who support Mr Trump's hardline stance. Scott Walker, Republican governor for Wisconsin tweeted a picture of the president walking to St.John's on Monday night with a caption that read: "Hard to image any other POTUS having the guts to walk out of the White House like this."
How the protests unfolded across the United States
But Trump is not without his supporters
There are, of course, many people in America who fully support their president's response to the protests.
In Upland, California, a small group of Trump supporters faced off to a peaceful crowds Black Lives Matter campaigners. One pulled a rifle from his vehicle and pointed it at the crowd and threatened the BLM protestors. The 39-year-old man was later arrested.
Trump also find unlikely support among rock stars; former Nirvana bassist Krist Novoselic declared the president's "law and order" speech.
“Wow!!! I know many of you can’t stand him, however, Trump knocked it out of the park with this speech,” Novoselic wrote in a message posted to his personal Facebook page.
While Novoselic acknowledged Mr Trump “should not be sending troops into states—and he legally might not be able to anyway,” the Nirvana bassist lauded the president’s tone as “strong and direct.”