The family of George Floyd appealed Tuesday for sweeping police reform on the anniversary of the African American man's murder by a white officer, as they met President Joe Biden at the White House.

The president and Kamala Harris, America's first female and first Black vice president, hosted several of Floyd's relatives in the Oval Office after the family spoke to top lawmakers hoping for progress on reform.

"The Floyd family has shown extraordinary courage," Biden said after their meeting -- declaring himself "hopeful" that a deal could be struck after the Memorial Day holiday this weekend.

The legislation being considered to increase police accountability would be named after Floyd, who suffocated after being pinned down under the knee of Minneapolis officer Derek Chauvin on May 25, 2020.

"If you can make federal laws to protect the bird, the bald eagle, you can make federal laws to protect people of color," Philonise Floyd, George's younger brother, said as he emerged from the private meeting, which lasted over an hour.

Another brother, Terrence Floyd, said as he left the White House that he was encouraged by the "productive conversation" in which Biden and Harris were eager to "actually give an ear to our concerns."

Floyd's mother, siblings and his daughter Gianna, along with family lawyers, had earlier gathered at the US Capitol with House Speaker Nancy Pelosi and other Democratic members of Congress.

While the adults discussed their hopes for police reform, it was seven-year-old Gianna -- hugging her mother Roxie Washington -- who eloquently addressed the legacy of her late father, saying he would "change the world."

"He did," Biden said after meeting the family nearly a year after their first encounter ahead of Floyd's funeral.

"I got a chance to spend a lot of time with Gianna and the family," he said. "They've been wonderful."

The family later visited Black Lives Matter Plaza close to the White House, which became a focal point for demonstrations in the weeks after Floyd's death.

"What's going on in America you can clearly see this right now, it's two justice systems -- so we need to get together as one," said Philonise Floyd. "Whatever I have to do to get this law passed, I will do, we want freedom, be able to walk in peace."

- Culture of impunity -

Floyd's 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.

Chauvin, who knelt on Floyd's neck for more than nine minutes as he passed out and died, is to be sentenced in June for murder and manslaughter.

In a sign Biden wants to confront head on what he sees as systemic racism, the White House announced the president will travel to Oklahoma on June 1 to mark the 100th anniversary of the Tulsa race massacre in which an estimated 300 Black men, women and children were killed.

In the wake of Chauvin's conviction last month, Biden sought to build on political momentum by urging Congress to pass a far-reaching police reform bill in time for the anniversary.

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

Despite missing Biden's deadline, Representative Karen Bass, a co-author of the reform bill, reiterated her commitment to Democrats and Republicans negotiating a compromise.

"We will get this bill on President Biden's desk," she said at the meeting with the Floyd family. "We will work until we get the job done."

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

Biden says a culture of impunity and underlying racism has made tragedies like Floyd's death increasingly common, although opponents believe police operating in often heavily armed communities are being scapegoated.

As if to highlight the staggering number of US shootings, multiple gunshots rang out Tuesday near the site in Minneapolis where people were marking the anniversary of Floyd's killing.

Shortly afterward a patient arrived at hospital suffering from a gunshot wound, police said.

- Ban on chokeholds -

The police reform bill would ban potentially fatal restraint techniques used on suspects, like chokeholds, and end so-called "no-knock warrants" that authorize police to burst into a suspect's house unannounced.

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

"My video didn't save George Floyd, but it put his murderer away and off the streets," Darnella Frazier, whose took crucial phone footage evidence of Floyd's death, said Tuesday in a Facebook post.

"I knew that he was another black man in danger with no power."