MINNEAPOLIS - A family friendly street festival, musical performances and moments of silence were held Tuesday to honor George Floyd and mark the year since he died at the hands of Minneapolis police on May 25, 2020, a death captured on wrenching bystander video that galvanized a global racial justice movement and continues to bring calls for change.

Mr. Floyd’s sister Bridgett and other family members held a moment of silence at a “Celebration of Life” event at a downtown Minneapolis park that included music, food trucks, an inflatable bouncy house and a vaccination stand.

A few miles away, at the site of the intersection where the 46-yer-old Mr. Floyd died, dozens of people kneeled for several minutes around a steel sculpture of a fist raised into the air. The somber time of the group on their knees symbolized the 9 minutes, 29 seconds during which Mr. Floyd was pinned to the pavement, his hands cuffed behind his back, by the knee of former Minneapolis Police Officer Derek Chauvin, who was convicted in April of Mr. Floyd’s murder.

Mr. Chauvin faces more than 40 years in prison when he is sentenced on June 25. Three other police officers who were fired still face trial.

“It’s been a troubling year, a long year,” Bridgett Floyd told the crowd in downtown Minneapolis. “But we made it. ... The love is here. George is here.”

Other members of Mr. Floyd’s family met in Washington with President Biden and Vice President Kamala Harris, who urged Congress to quickly pass a law in Mr. Floyd’s name that would bring changes to policing.

Amoment of silence to honor Mr. Floyd also was held in New York and a rally was held in Los Angeles. Globally, a rally took place in Germany and Mr. Floyd’s death was marked by U.S. embassies in Greece and Spain that placed large Black Lives Matter banners on their facades.

Hours before the Minneapolis festivities, the intersection where Mr. Floyd died was disrupted by gunfire. Video from 38th Street and Chicago Avenue — informally known as George Floyd Square — showed people running for cover as shots rang out. Police said a man, who they believe was injured in the shooting, went to a nearby hospital with a gunshot wound. Police said he was in critical condition but was expected to survive. There were no immediate arrests.

Like other major cities, Minneapolis has been struggling with rising gun violence, a problem made worse, in part, by many officers leaving the embattled force since Mr. Floyd’s death. A 6-year-old girl was fatally shot and two other children were wounded in recent weeks.

Minneapolis Mayor Jacob Frey last week unveiled sweeping public safety proposals aimed at fixing the problem. Other groups are pursuing a more radical remaking of the police department.

The intersection of 38th and Chicago has been barricaded since soon after Mr. Floyd’s death. It quickly turned into a me- morial site and was transformed Tuesday into an outdoor festival, with food, children’s activities and music. Artwork and signs from protests after Mr. Floyd’s death also were on display. One group hosted an open mic next to a greenhouse that community members constructed earlier this year to house flowers left by mourners. Nearby, a brass band played for passers-by.

The celebration also included a candlelight vigil, capping several days of marches, rallies and panel discussions about his death and confronting racial discrimination.

Xavier Simmons, 24, from Racine, Wis., chanted “Say Mr. Floyd’s name!” as people kneeled. Mr. Simmons said he hopes people taking part in the festivities will both honor Mr. Floyd’s life and legacy and continue to “uplift and empower this movement.”

“We got the verdict that we needed, but it’s never going to change until we make a change,” he said.

“Y’all keep doing the work because y’all changing the world,” Common, the award-winning rapper, actor and activist, told the crowd of hundreds during a musical performance Tuesday night prior to the vigil.

After Common left the stage and day turned to night in George Floyd Square, people placed candles in every conceivable corner, lighting up the area.

Earl Vaughn, 20, of Minneapolis, attended the downtown event and said despite its celebratory atmosphere: “For all this a Black man had to die, so that’s really unfortunate.”

In New York City, elected officials, including Mayor Bill de Blasio and U.S. Rep. Hakeem Jeffries, joined the Rev. Al Sharpton in kneeling for 9 minutes, 29 seconds.

“As we took a knee, imagine how long that was on a human being’s neck,” Rev. Sharpton said. “Never switched knees, just dug in. It’s time we correct policing in this country.”

On Tuesday evening, activists and demonstrators gathered with some families of people who had died in interactions with the New York Police Department at Barclays Center in Brooklyn, N.Y. They called for defunding the police, holding officers accountable and removing police officers from schools. Following the rally, they set off on a march through Brooklyn streets.

Several Floyd family members, including his 7-year-old daughter Gianna, met with President Biden and Vice President Harris earlier Tuesday. President Biden, who previously pledged to continue fighting for racial justice, said he hopes the U.S. Senate can quickly pass the George Floyd Justice in Policing Act and get it to his desk.

“We have to act,” he said of the legislation that would ban chokeholds and no-knock police raids and create a national registry for officers disciplined for serious misconduct.

Mr. Floyd’s brother Philonise told CNN he thinks about George “all the time.”

“My sister called me at 12 o’clock last night and said, ‘This is the day our brother left us,’ ” he said, adding: “I think things have changed. I think it is moving slowly but we are making progress.”

Also Tuesday, the U.S. Senate voted to confirm Kristen Clarke as assistant attorney general for civil rights, the first Black woman to hold the position. In the last few weeks, the U.S. Justice Department under President Biden has announced sweeping investigations into the police in Minneapolis and Louisville and brought federal civil rights charges against the officers involved in Mr. Floyd’s death.

Separately, the Floyd family announced the launch of a fund that will make grants to businesses and community organizations in the neighborhood, as well as broader grants “encouraging the success and growth of Black citizens and community harmony.” The money comes from $500,000 earmarked as part of the city’s $27 million civil settlement for the Floyd family.