George Floyd’s family met Joe Biden at the White House one year after Mr Floyd’s death as the president reflected on “the hard reality that racism has long torn us apart”.

This first anniversary was supposed to be a milestone moment in Washington, a time to mark the passage of a policing law to make criminal justice more just.

Instead, Mr Floyd’s family met Mr Biden and vice president Kamala Harris not only to commemorate their loss but to continue the push for legislation.

“It was a remembrance of what happened to my brother,” Philonise Floyd said of the meeting with Mr Biden, calling the president “a genuine guy”.

Mr Biden told them “he just wants the bill to be meaningful and that it holds George’s legacy intact”, said George Floyd’s nephew Brandon Williams, adding Mr Biden showed “genuine concern” for how the family was coping.

Mr Biden took time during the meeting to play with George Floyd’s young daughter Gianna, who enjoyed some ice cream and Cheetos, the president said, after she told him she was hungry.

Later, she stood before the cameras outside the White House and softly called out “Say his name”. Family members chanted “George Floyd” in return.

A sister, Bridgett Floyd, stayed away, aiming to come to Washington only when there is a bill to be signed into law.

“That’s when I will make my way to DC,” she said from Minnesota.

She and several more family members joined Minneapolis Mayor Jacob Frey and others marking the anniversary in the city where George Floyd died, as other events took place in New York, Los Angeles and other cities in the US and elsewhere.

Speaking to reporters at the end of the day, Mr Biden said he had spoken with congressional negotiators and was “hopeful that sometime after Memorial Day we’ll have an agreement”.

With the proposed George Floyd Justice in Policing Act still pending, his family began the day meeting with legislators and headed back to Capitol Hill later from the White House.

They met on Tuesday morning with Democratic House Speaker Nancy Pelosi and Democratic Representative Karen Bass, who ushered the bill through the House.

The Floyds met late in the day with Democrat Cory Booker of New Jersey and Republican Tim Scott of South Carolina, the Senate’s lead negotiators on the bill. The family then visited Black Lives Matter Plaza, the site near the White House where protesters gathered throughout last summer.

“I was pleasantly surprised and encouraged by their thoughts,” Mr Scott said of the family. “I wish I was negotiating with them,” he said, though he also repeated the line of the day that progress was being made.

Earlier at the Capitol alongside Ms Pelosi and other politicians, Philonise Floyd declared of his brother: “Today is the day that he set the world in a rage.

“We need to be working together to make sure that people do not live in fear in America any more.”