Hours after President Trump stood on the South Lawn of the White House to rail against what he called agitators bent on destroying “the American way of life,” thousands of Americans streamed to the Lincoln Memorial, not a mile away, on Friday to deliver what frequently seemed to be a direct reply.

The march was devised in part to build on the passion for racial justice that the Rev. Dr. Martin Luther King Jr. summoned when he delivered his “I Have a Dream” address on that same spot 57 years ago. From the lectern at the base of the memorial, civil rights advocates and Black ministers often cast Mr. Trump as the prime obstacle to their goal, and voting to remove him as the first step toward a solution.

Dr. King’s eldest son, Martin Luther King III, described Mr. Trump as “a president who confuses grandiosity with greatness” and opts for chaos over community.

“We need you to vote as if your lives, our livelihoods, our liberties depend on it. Because they do,” he told the crowd. “There’s a knee upon the neck of democracy, and our nation can only live so long without the oxygen of freedom.”

The Rev. Al Sharpton invoked Jacob Blake, who was shot by a police officer in Kenosha, Wis., on Sunday, and the Black shooting victims before him to demand a new national reckoning with hate and bigotry.

“We didn’t come to start trouble,” he said, in an implicit rebuke to critics of the summer’s racial protests. “We came to stop trouble. You act like it’s no trouble to shoot us in the back. You act like it’s no trouble to put a chokehold on us while we scream ‘I can’t breathe’ 11 times.

“Mr. Trump, look right down the block from the White House,” he added. “We’ve come to Washington by the thousands.”

With the march coming just after the conclusion of the Republican National Convention, the two events presented starkly different accounts of the state of the country in a summer marked by widespread protests of police officers killing Black people and a pandemic that has taken about 181,000 lives and cost millions of jobs.

The Republicans mentioned Mr. Blake, who is partially paralyzed in a hospital, or other Black victims only in passing, and painted a picture of American cities out of control, with police officers restrained from containing violence instigated by protesters.

Rudolph W. Giuliani, the former New York City mayor and Mr. Trump’s personal attorney, claimed that police officers were “handcuffed by progressive Democrat mayors from doing anything but observe the crimes and absorb the blows.”

For the thousands who came to the Lincoln Memorial on Friday, the country’s problem was not too little police presence but far too much.

The parade of speakers included family members of Mr. Blake and others who were shot in encounters with the police. They drew roars of approval from listeners, some of whom came hundreds of miles from Ohio, Georgia, Arizona and elsewhere.

“There are two systems of justice in the United States,” Mr. Blake’s father, Jacob Blake Sr., told the crowd. “There’s a white system and there’s a Black system. The Black system ain’t doing so well.”

Senator Kamala Harris of California, the Democratic vice-presidential candidate, recorded a message that drew huge cheers from the protesters when it was played on large screens around the memorial.

“The road ahead, it is not going to be easy,” she said. “But if we work together, to challenge every instinct our nation has to return to the status quo, and combine the wisdom of longtime warriors for justice with the creative energy of young leaders today, we have an opportunity to make history, right here and right now.”

Among the listeners was Ruby Williams, 67, a retired corrections officer from Frederick, Md., who said she was voting for Mr. Trump’s opponent, former Vice President Joseph R. Biden Jr., in November.

“It’s good against evil at this point,” she said.

The protest, held at the peak of the capital’s stifling heat and humidity, began shortly after sunrise as knots of demonstrators clustered in front of the Lincoln Memorial. It ended in the afternoon with a march by a flood of protesters, stretching nearly a half-mile along the reflecting Pool, to a national memorial honoring Dr. King at the Tidal Basin.

Dr. King’s March on Washington for Jobs and Freedom drew an audience of a quarter-million in 1963. The Commitment March on Friday did not approach that number, in part because the city is requiring quarantines for visitors from 27 states. A permit issued by the city on Tuesday had indicated that 50,000 people might attend. Much of the event was streamed live on the internet or broadcast.

Attendees were screened for fever and required to wear masks, and were told to stay apart to reduce the risk of coronavirus infection. Placards peppering the area warned of the risk of Covid-19 and urged people to use the hand sanitizer stations. But as the crowd swelled, social distancing clearly became difficult, and at least one speaker urged the audience to take greater care.

Organizers said the size of the crowd was less important than the event’s goals, including increasing voter registration and participation in the 2020 census and enacting a new version of the Voting Rights Act of 1965.

The protest also sought to rally support for enacting the George Floyd Justice in Policing Act, backed by House Democrats and the Congressional Black Caucus. The bill would overhaul law enforcement training and conduct rules to try to limit police misconduct and racial bias.

The national upheaval triggered by Mr. Floyd’s death at the hands of the Minneapolis police in May loomed large over the march, as did the sense among civil rights leaders that action this year could set the course of American race relations for years, if not decades.

“We can’t ignore the moment that we’re in,” said Kristen Clarke, the president of the Lawyers’ Committee for Civil Rights Under Law, one of several groups that sponsored the protest. “This is a march that is very much needed right now, given the fires that are raging as we deal with police violence, racial violence and voter suppression. It’s created almost a perfect storm.”

The march “has to be understood as a moment for which these protests must lead to something,” said Marc Morial, the former New Orleans mayor who is president of the National Urban League, another sponsor of the march. “So it must lead to significant policy change. Structural racism is not addressed with talk or good will alone.”

On Friday, speaker after speaker hammered home the consequences of failing to follow a feel-good protest with action.

Mr. Floyd’s brother Philonise Floyd struggled to tell listeners that “everyone here has made a commitment because they wouldn’t be here for any other reason right now. Because it’s hot, it’s hot.” He paused, overcome, and told those around him: “Man, it’s hard. Man, it’s really hard.”

“What will be our legacy?” asked Bridgett Floyd, George Floyd’s sister. “Will our future generations remember you for your complacency or your inaction? Or will they remember you for your empathy, your leadership, your passion for weeding out the injustice and evil in our world?”

Eric Porter, 50, said he had left his home in New Jersey early Friday, driving through the night to reach the protest. Mr. Porter said he had never previously marched for a cause, but after the shooting of Mr. Blake he felt that he and his 15-year-old son needed to witness the event.

“We’ve had a sleeping giant where racism was under the radar and we thought we’d overcome it,” he said, “but this president we have, he’s woken up those demons that we thought were dead, and I’m seeing it.”

And Ephraim Adamz, 35, a filmmaker from Hartford, Conn., said his 83-year-old grandmother had attended the 1963 March on Washington but could not return because of the pandemic. He said he had come in her stead.

“It’s our job as young people to do what the elderly can’t do,” he said, adding that he was posting video of the protest on Facebook Live “so she can watch it later.”

The crowd grew hushed when Yolanda Renee King, the 12-year-old daughter of Martin Luther King III, issued a fiery and poised call for her generation to pick up her grandfather’s torch.

“I want to call on the young people here to join me in pledging that we have only begun the fight, and that we will be the generation that moves from ‘me’ to ‘we,’” she said. “We are going to be the generation that dismantles systemic racism for once and for all, now and forever.”

It was a ringing note of optimism on a day when was impossible to ignore that 57 years of marches and action had yet to realize Dr. King’s dream.

“This feels different than other times,” said Lyn Ledbetter, 43, from Phoenix, who attended the march with her sister Aisha Magee, of Atlanta, and Ms. Magee’s 10-year-old son. ”Maybe I’m just being optimistic, but we’ve been too complacent before. This generation feels different.”