Relatives of Michael Brown, shot dead in the Missouri town of Ferguson, and Eric Garner, who died being restrained in New York, were among them.
Both died after encountering police, but grand juries decided not to bring charges, sparking anger and unrest.
Another demonstration in New York also drew thousands despite chilly weather.
Speakers at the Capitol called for changes to US legislation.
Lesley McSpadden, mother of Michael Brown, told the crowd: “What a sea of people. If they don’t see this and make a change, then I don’t know what we got to do. Thank you for having my back.”
The mood in Washington DC was described as calm but defiant, with a large number of police on standby.
Earlier in the day, a small group of protesters from Missouri disrupted the schedule by taking to the stage at the starting-point, on Freedom Plaza, and blowing a bullhorn.
They complained that the protest, which was organized by long-established civil rights groups, was staid and ineffective.
Michael Brown, 18, was shot dead on August 9 during an altercation with a white police officer in Ferguson, Missouri.
Eric Garner, 43, died while being held down by a white police officer on July 17.
He had been challenged over the alleged sale of loose cigarettes on a street in Staten Island, New York.
The event was caught on camera and his dying plea of “I can’t breathe” has become a slogan of the protesters. It echoes the adoption of “Hands up! Don’t Shoot!” – a Ferguson refrain alleging that Michael Brown was surrendering to police when the fatal shots were fired.
Relatives of three other black people killed in controversial shootings were also expected to attend the march, according to the National Action Network:
Marchers crowded Pennsylvania Avenue for the walk from Freedom Plaza to the Capitol, but the actual numbers were not immediately clear.
Some in the crowd, which was made up of both black and white people, held banners saying: “Stop racist police”, “I can’t breathe”, and “President Obama seize this moment. The ancestors are watching.”
The Rev Al Sharpton, a leading civil rights advocate, called for “legislative action that will shift things both on the books and in the streets”.
MPuFym61C3AThe US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…