Floyd's death set off protests around the world, including outside the White House.
Afterwards, the video shows a compilation of shops being destroyed during the last week, with the president saying the memory of Floyd is being "dishonored by rioters, looters and anarchists".
Claiming improvements everywhere, Trump said, "Hopefully George is looking down right now and saying this is a great thing that's happening for our country".
The US unemployment rate dropped unexpectedly in May, but not all workers benefited equally as joblessness among African Americans and Asians rose, signaling some minorities face a longer recovery as the economy slowly rebounds from the coronavirus shutdowns.
"For the president to try to put any other words in the mouth of George Floyd, I frankly, think is despicable", Biden said at an event in Delaware. This is a great day in terms of equality. The White House called such an interpretation "false".
However, dozens of media outlets took Trump's "great day" comments and framed them as though George Floyd should be happy about the jobs report.
Construction, healthcare and retail also added jobs in what proved to be a record monthly employment gain of 2.5 million jobs on the heels of April's record loss of 20.7 million positions. Economists had been expecting them instead to slash 8 million jobs in continuing fallout from the pandemic.
The jobless rate, at 13.3%, is still on par with what the nation witnessed during the Great Depression. Joe Biden, his presumptive Democratic opponent in the November election, immediately lashed out at Trump for invoking Floyd's name, calling it "despicable".
"Let's be clear about something: The depth of this jobs crisis is not attributable to an act of God but to a failure of a president", Biden declared in a DE speech shortly after Trump spoke. He said Trump was referencing the "national conversation" that followed Floyd's death and "Americans coming together on the belief that everyone should be treated equally under the law". "Now is not the time to be complacent or take a victory lap", Senate Minority Leader Chuck Schumer said. It did not say who made the complaint. More than 1.88 million Americans have been infected and more than 108,000 have been killed by the virus since February.
Before that, Trump's mood was largely ebullient even though the number of Americans who have died coronavirus-related deaths approaches 110,000, according to a tally from Johns Hopkins University.
Now, though, Trump said states and cities should be lifting remaining restrictions. "I don't know why they continue to lock down", he said of some jurisdictions that have maintained closings.
But there was little sign of concern among Trump and his Republican allies in Washington.
"As per our copyright policy, we respond to valid copyright complaints sent to us by a copyright owner or their authorized representatives", a Twitter spokesperson said in a statement on Friday. He added: "Today is probably the greatest comeback in American history".