President Biden, who has suffered several personal losses himself, said in a statement he related to the Floyd family in their first year of loss, as they relived Floyd's death with every play of the video of his arrest.

"The Floyd family has shown extraordinary courage, especially his young daughter Gianna, who I met again today," the president added.

Biden reiterated his support for the George Floyd Justice in Policing Act and appreciated "the good-faith efforts from Democrats and Republicans to pass a meaningful bill out of the Senate." He called on Congress to act quickly to pass the legislation.

"We face an inflection point. The battle for the soul of America has been a constant push and pull between the American ideal that we’re all created equal and the harsh reality that racism has long torn us apart," Biden said.
-ABC News' Molly Nagle

Attorney Benjamin Crump told reporters outside the White House following a meeting between President Biden and the Floyd family that the president is not looking for a "rushed" bill.

"He said that he doesn't want to sign a bill that doesn't have substance and meaning, so he is going to be patient, to make sure it's the right bill," Crump said.

Philonise Floyd, George's brother, pleaded with Congress to pass the George Floyd Justice in Policing Act.

"If you can make federal laws to protect the bird which is the bald eagle, then you can make federal laws to protect people of color," he said.

Floyd's daughter, Gianna, led the call to “say his name” before leaving the White House.

-ABC News' Libby Cathy and Molly Nagle

Floyd’s family, along with their attorney, Benjamin Crump, attended a closed meeting with President Joe Biden at the White House Tuesday afternoon.

President Biden and his team have been “closely engaged” with negotiators on the George Floyd bill but are “respecting the space” negotiators need to work out the details, White House press secretary Jen Psaki told reporters Tuesday afternoon.

Prior to meeting the president, Floyd’s family also spoke with House Speaker Nancy Pelosi and Rep. Karen Bass.

"What we hope to do at all of those meetings is to continue to say, let's don't lose this moment. It's been 57 years since we've had meaningful police reform," Crump said Tuesday morning on SiriusXM’s “The Joe Madison Show.” "And this is our moment to finally pass some federal legislation with teeth in it."

The Floyds, along with NAACP President Derrick Johnson, are also set to meet with Sen. Cory Booker, D-N.J., and Sen. Tim Scott, R-S.C.

"It is critical that the bill is substantive and that we get it right," Johnson said in a statement Tuesday. "We want the right bill, not a rushed bill."

Congressional Black Caucus Chair Joyce Beatty called on the Senate to pass the George Floyd Justice in Policing Act in a new statement released Tuesday.

Beatty named other Black Americans who were killed by the police in the last couple of years, including Breonna Taylor, Daunte Wright, Adam Toledo, Andre Hill, Casey Goodson Jr., Ma’Khia Bryant and Tamir Rice.

"Unfortunately, nothing will ever bring them back or undo the unimaginable heartache and loss their family, friends, and our communities have had to endure, but we can turn agony into action," Beatty said in a statement. "The American people are demanding change, transparency, accountability, and equal justice."

-ABC News' Beatrice Peterson