President Joe Biden marks the anniversary Tuesday of the police murder of George Floyd by hosting the African-American man's family at the White House -- but without being able to celebrate hoped-for national police reform.

Floyd's daughter Gianna, his mother, sister and brothers will be among those attending a private meeting with Biden, Press Secretary Jen Psaki said.

"The courage and grace of his family, and especially his daughter Gianna, has really stuck with the president," Psaki told reporters. "He's eager to listen to their perspectives."

Former Minneapolis policeman Derek Chauvin, who knelt on Floyd's neck for more than nine minutes until he passed out and died, was convicted of murder last month and is to be sentenced in June. 

Floyd's May 25, 2020 death sparked protests against racial injustice and police brutality across a country already crackling with tension from the election battle between Biden and Donald Trump.

In the wake of the verdict, Biden sought to build on political momentum by urging Congress to pass a far-reaching police reform bill in time for the first anniversary.

Americans must confront the "systemic racism" revealed by Floyd's killing "head on," he declared.

However, the ambitious deadline comes with only the House having passed the bill, known as the George Floyd Justice in Policing Act, while the Senate continues to wrangle over key details.

Before heading to the White House, the Floyd family will meet Democratic House Speaker Nancy Pelosi and Representative Karen Bass, the lead House negotiator on the reform bill.

The Act seeks to reform what critics say have become ever more violent and unaccountable police forces around the country.

Opponents argue that police are being unfairly blamed when they are simply trying to operate in a dangerous and often heavily armed society. 

However, Biden and reform proponents say that a culture of impunity and underlying racism have made incidents like Floyd's death increasingly common.

Personal impact on Biden 

Among other measures, the bill would ban potentially fatal restraint techniques used on suspects, like chokeholds.

It would also end so-called "no-knock warrants," when police are authorized to burst into a suspect's house unannounced -- a volatile situation that led to the accidental killing of a Black woman, Breonna Taylor, in Louisville, Kentucky, in March 2020.

The most far-reaching of the measures that senators are still debating would be to end current legal protections that block civil lawsuits against police accused of misconduct.

Psaki put a brave face on chances of success, saying that "the president is still very much hopeful that he will be able to sign the George Floyd Justice in Policing Act into law."

While nothing is easy to get through the heavily divided Congress, Biden hopes that the energy unleashed in the wake of Floyd's death will "help move this legislation across the finish line."

Confirming that there is still hope for the bill, Bass, Democratic Senator Cory Booker and Republican Senator Tim Scott issued a joint statement on Monday citing "progress."

"This anniversary serves as a painful reminder of why we must make meaningful change. While we are still working through our differences on key issues, we continue to make progress toward a compromise and remain optimistic," they said.

After meeting Biden, the Floyd family will hold talks Booker and Scott and pay a visit to "Black Lives Matter Plaza" near the White House.

For Biden himself, hosting the Floyds for a "real conversation" will be a moving moment, Psaki said.

George Floyd's death was "a day that certainly impacted him personally and impacted millions of Americans."