The US president spoke nearly an hour during the press briefing on Friday morning, only briefly mentioning Mr Floyd, the 46-year-old black man who died on May 25 after a white police officer pressed his knee on his neck for nearly nine minutes.
"Hopefully George is looking down right now and saying there’s a great thing happening for our country," Trump said, saying that an economic rebound "is the greatest thing that can happen for race relations."
"It’s a great day for him. It’s a great day for everybody."
He added: "Equal justice under the law must mean that every American receives equal treatment in every encounter with law enforcement, regardless of race, colour, gender or creed.
"They have to receive fair treatment from law enforcement. They have to receive it. We all saw what happened last week. We can't let this happen."
Trump, far off script, talking about jobs numbers and equality and who knows what: “Hopefully, George is looking down right now and saying, this is a great thing happening in our country.” pic.twitter.com/ul6RG5wozK— The Recount (@therecount)June 5, 2020
The death of Mr Floyd last month touched off the most serious wave of civil unrest in the US since the assassination of Martin Luther King Jnr in 1968.
From Paris and London to Tel Aviv, Sydney, Johannesburg and Rio de Janeiro, the killing has also prompted demonstrations across the world, with protesters decrying inequality, police brutality and other problems in their own countries.
During the press briefing at the White House, Mr Trump celebrated a US employment report which showed the country gained more than 2.5 million jobs last month during the thick of the coronavirus pandemic, and predicted the battered economy will have recovered by 2021.
I had to clip this because it is unbelievable. President @realDonaldTrump just said this: “Hopefully, George is looking down right and saying this is a great thing that’s happening for our country. It’s a great day for him, it’s a great day for everybody.” #GeorgeFloyd pic.twitter.com/6CbGoLJrRg— Vladimir Duthiers (@vladduthiersCBS)June 5, 2020
"We're bringing our jobs back," Mr Trump said. "I think we're actually going to be back higher next year."
Trump pitched himself as key to what he claimed would be a "rocket ship" economic rebound, and offered that as an argument for his reelection in November.
"I'm telling you next year, unless something happens or the wrong people get in here, this will turn around," Trump said.