Biden says he told George Floyd's daughter, Gianna, her father "changed the world" ... and he's calling on Americans to unite behind the guilty verdict and help make the country a better place where folks don't have reason to fear law enforcement.

POTUS says Floyd's murder in broad daylight ripped the blinders off and allowed the world to see the systemic racism rooted in America ... and Biden says the verdict is a step towards changing the country's trajectory.

Harris says the guilty verdict offers a bit of relief, but it can't bring back Floyd or take away his family's pain ... and she says now's the time to reform policing in America.

In the courthouse hallway moments after the verdict, Biden called the Floyd family and expressed his feelings that justice was served.

As you know by now, a Minneapolis jury just found Chauvin guilty of second-degree murder and third-degree murder for killing Floyd during his arrest on May 25, 2020. Chauvin was also found guilty of second-degree manslaughter.

Earlier on Tuesday, the Prez commented that he had checked in on Floyd's family and told them he was "praying the verdict is the right verdict." He also called the Chauvin case "overwhelming."

The Chauvin verdict does not mean the overwhelming nature of the case is over ... as the 3 other officers involved in Floyd's arrest are due to stand trial soon as well.