By Jason Hanna and Harmeet Kaur, CNN

(CNN) -- Fifty-seven years to the day Martin Luther King Jr. gave his "I Have a Dream" speech, relatives of African Americans killed or injured in recent police encounters took to the same spot on the National Mall to emotionally call for social and political change.

"We will not be a footstool to oppression, "Jacob Blake's sister, Letetra Widman, said to crowds in front of the Lincoln Memorial in Friday's March on Washington.

"Black America, I hold you accountable. You must stand. You must fight, but not with violence and chaos," she said.

Numerous speakers, including King's son Martin Luther King III, made emphatic calls for police reform, justice reform and voter action in an event meant to recall the 1963 March on Washington that demanded civil rights and economic opportunity.

Friday's event, dubbed the "Commitment March: Get Your Knee Off Our Necks," was organized by the Rev. Al Sharpton, who announced the march on June 4 as he delivered a eulogy for George Floyd, a Black man who died in police custody in Minneapolis.

"My brother cannot be a voice today. We have to be the voice. We have to be the change," George Floyd's sister, Bridget Floyd, said Friday.

"We're at a point we can get that change," Breonna Taylor's mother, Tamika Palmer, said, "but we have to stand together -- we have to vote."

The event brings an end a tumultuous week, one that saw Blake shot by police in Wisconsin. It follows a summer that has seen a global outcry over the killings of Black Americans at the hands of law enforcement. And it takes place in the midst of a pandemic that has disproportionately affected people of color.

Speakers called on the Senate to pass police reform legislation named after Floyd, which the House approved in June. And they called for ending police violence, dismantling systemic racism and ensuring access to the ballot box, organizers said.

The bill -- titled the George Floyd Justice in Policing Act of 2020 -- would overhaul qualified immunity for law enforcement, prohibit no-knock warrants in federal drug cases, ban chokeholds at the federal level and establish a national registry of police misconduct, among other provisions.

King III spoke against police brutality and for voter action -- and called on people to do more than quote his slain dad.

"If you're looking for a savior, get up and find a mirror. We must be (our own) hero," by voting and working for social change, King said.

"Raise our voices and say, 'Enough is enough!'" he said.

Sharpton called for America to never "forget what you've done," referring to police shootings of African Americans. "Call their names."

"Society had (its) knee on our neck," he said. "We are rising up. We are going to get your knee off our neck!"

A march to the Martin Luther King Jr. Memorial

Crowds gathered around and in front of the memorial's reflecting pool. Closer to the podium, some people sat in chairs, spaced feet apart for coronavirus precautions, on the plaza.

Organizers stressed that the march would comply with health guidance and local ordinances. Face masks are required to march, and masks, gloves and hand sanitizer will be provided on site.

Crowds, after the speeches, were to march about a half-mile away to the Martin Luther King Jr. Memorial.

Organizers said the event was meant to be a commemoration of a seminal moment in US history, one that demanded civil rights and economic opportunity.

Activists there called on the Senate to pass police reform legislation named after Floyd, which the House approved in June. And they're calling for ending police violence, dismantling systemic racism and ensuring access to the ballot box, organizers said.

The bill -- titled the George Floyd Justice in Policing Act of 2020 -- would overhaul qualified immunity for law enforcement, prohibit no-knock warrants in federal drug cases, ban chokeholds at the federal level and establish a national registry of police misconduct, among other provisions.

They also raised concerns about disenfranchisement, citing policy changes at the US Postal Service, along with President Trump's efforts to discredit mail-in voting

'It's a huge moment for us as a people'

A Black man who traveled from Dallas to attend was there because "it's a huge moment for us as a people," he told CNN affiliate WJLA.

"Fifty-seven years ago, they were here marching on Washington for just equality as a people. Right now, I think this march is about survival," the man, who gave his name only as Bubba, said.

"There's no waiting for us to vote. We shouldn't have to wait for that. That should happen today, to where we shouldn't have to be out worried about our kids ... without having to worry about getting a phone call that they have been shot or killed, especially by police that supposed to protect us," he said.

Ahead of the main program, recorded messages were played on large screens in front of the memorial, in which speakers called for people to vote and, as one speaker said, "to make those who are comfortable with our oppression uncomfortable."

Martin Luther King III: 'Dad would be very proud'

Before the event, Martin Luther King III told CNN that "Dad would be very proud that people are coming together to stand up against injustice."

"But certainly (he would be) very sad that we're still attempting to get justice."

Adding to the urgency for organizers is the November election, the lead-up to which has been marked by a divisive presidential campaign.

Trump has downplayed police violence against Black Americans and characterized protests in US cities as a descent into lawlessness.

Given the momentum of the Black Lives Matter movement, King says he is optimistic that tides are turning.

"We are on the way to a resolution, I believe, because the consciousness is awakened," King told CNN before the march. "I don't think these young people are going to stop. I think they're going to continue to demand justice."

Marchers are evoking spirit of John Lewis

Friday's march also honored the late civil rights icon and congressman John Lewis, who spent his life fighting for voting rights.

At 23, Lewis was one of the youngest keynote speakers at original march in 1963. He was also its last surviving speaker.

"We're walking in the spirit of Dr. King but also in the spirit of John Lewis to make 'good trouble,'" Tylik McMillan, the national director of youth and college for Sharpton's National Action Network (NAN), told CNN last week.

Activists are building on Lewis' legacy by calling on the Senate to pass a voting rights bill named after him. The measure, passed by the House in December, would restore a key part of the historic Voting Rights Act that the Supreme Court struck down in 2013.

NAN is also encouraging attendees to fill out the 2020 US Census, register to vote, and sign up to be poll workers and monitors.

The Black National Convention will follow

Months before Sharpton announced this year's march, the Movement For Black Lives (M4BL) -- a coalition of progressive Black organizations -- was already at work planning another gathering: the Black National Convention.

That event is also happening on Friday, and takes inspiration from the 1972 Black National Convention in Gary, Indiana.

The virtual convention will be broadcast live starting at 7 p.m. ET and will feature conversations, performances and other programming aimed at mobilizing Black communities.

The event was envisioned as a space where progressive Black organizers could engage outside of the major political parties and discuss policy solutions "without giving up their radical beliefs and values," said Jessica Byrd, co-founder of the Electoral Justice Project of M4BL.

"Black people have been saying for literal decades that we want a meaningful place inside of the national political dialogue, and meaningful means specific public policy solutions that meet the height of the need and the height of the problem," Byrd told CNN. "We have yet to have it in this country, on any side."

Activists will also ratify a policy agenda on police reform, criminal justice reform and other issues, just after the Republican National Convention and Democratic National Convention.

M4BL supports several policy positions that are more radical than the ones organizers of Friday's march are currently demanding. Among them is the Breathe Act, which would divest federal resources from police and invest them into healthcare, alternative community safety solutions and other sectors.

But while there may be some generational differences between the march and the Black National Convention, Byrd said the packed day of events is a sign of the political moment we are in.

"As Al Sharpton announced the march, we immediately thought, 'Well, it's going to be the best, Blackest political weekend to end this Freedom Summer,'" Byrd told CNN. "And that's a good thing for all of us, and in particular, Black voters."