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

Minnesota Attorney General Keith Ellison released a statement Tuesday stating that black people have been dying at the hands of police for the past century and the time for "meaningful change" is now.

"African American communities have been gaslit by people in authority for 100 years: they have been repeatedly told that state-sanctioned violence in their communities is their fault and that they are the criminals, not the ones committing the crimes against them," Ellison said. "But this time, the witnesses to George Floyd’s death and everyone in the world who watched their videos refused to be gaslit. They believed their eyes."

Ellison called on legislators on every level to break the cycle and for Americans of all backgrounds to end racism and white supremacy once and for all.

"For a century, and despite the best efforts of many, America has chosen inaction over climbing this mountain," Ellison said. "But the other side of this mountain is better — not only for African Americans, but for everyone."

-ABC News’ Whitney Lloyd