Thousands of protesters have marched across the US to call attention to the deaths of unarmed black men at the hands of police and urge lawmakers to take action.

Demonstrators went past the White House in Washington DC, along iconic Fifth Avenue in New York and through the middle of Nashville's honky-tonk district.

Chanting "I can't breathe!" ''Hands up, don't shoot!" and waving signs reading "Black lives matter!" the demonstrators also staged "die-ins" as they lay down across intersections, and in one city briefly blocked an on ramp to a motorway.

Esaw Garner, widow of Eric Garner, 43, who died in July after being put in a chokehold by a New York City police officer during an arrest for allegedly selling loose, untaxed cigarettes, said: "My husband was a quiet man, but he's making a lot of noise right now."

Speaking from the Washington DC protest, she added: "His voice will be heard. I have five children in this world and we are fighting not just for him but for everybody's future, for everybody's past, for everybody's present, and we need to make it strong."

Organisers had predicted 5,000 people at the Washington march, but the crowd appeared to far outnumber that. They later said they believed as many as 25,000 had shown up.

Mr Garner's mother, Gwen Carr, called the demonstrations a "history-making moment".

"It's just so overwhelming to see all who have come to stand with us today," she said. "I mean, look at the masses. Black, white, all races, all religions. ... We need to stand like this at all times."

Joining the Garners in Washington were speakers from the family of Tamir Rice, a 12-year-old killed in Ohio as he played with a pellet gun in a park, and the Reverend Al Sharpton, a leading civil rights activist, who helped organise the marches.

"Members of Congress, beware we're serious ...," Rev Sharpton said. "When you get a ring-ding on Christmas, it might not be Santa; it may be Rev Al coming to your house."

Several speakers asked the crowd to chant, "I can't breathe." Garner, 43, had gasped those words before his death. Some protesters also wore those words on shirts. Other speakers called for a chant of "Hands up, don't shoot," and protesters also waved signs reading "Black Lives Matter!"

The chant about raised hands has become symbolic of the protests that erupted after 18-year-old Michael Brown's shooting death by a white police officer in Ferguson, Missouri, although there was conflicting witness evidence about whether Brown actually had his hands raised in surrender - or was charging at the officer - when he was fatally shot.

Just before the crowd marched to the Capitol, the rallying was interrupted briefly by more than a dozen protesters who took the stage with a bullhorn. They announced that they were from the St Louis area and demanded to speak.

"This movement was started by the young people," said Johnetta Elzie, who ultimately was allowed by rally organisers to speak.

Organisers called the interruption unnecessarily divisive. But some in the Missouri group, mostly in their 20s, said they were disappointed and found the rally staid and ineffective.

"I thought there was going to be actions, not a show. This is a show," Ms Elzie said.

Protests, some violent, have occurred around the US since grand juries in New York and Missouri last month declined to indict the officers involved in the deaths of Mr Brown and Mr Garner. Before the crowd started marching, Rev Sharpton directed, "Don't let no provocateurs get you out of line. ... We are not here to play big shot. We are here to win."

Then, blocks of tightly packed people moved through the city.

Among the large crowds on New York's Fifth Avenue were family members of people killed by New York City police going back decades.

Donna Carter, 54, marched with her boyfriend, whose teenage son was shot and killed by police in the 1990s while carrying a toy gun.

"It's good to see people of all colors here to say enough is enough," said Ms Carter. "I'm a parent and every child that's killed feels like my child."

Others were there to show their outrage, including Rich Alexandro, 47, who carried a handmade sign with dozens of names of victims of police killings in which officers were never charged.

Politicians and others have talked about the need for better police training, body cameras and changes in the grand jury process to restore faith in the legal system.

DC police chief Cathy Lanier said the Washington march was peaceful. She mingled with the crowd and said she wanted to show solidarity with the marchers.

"This is one of the most well-organised events I've seen," Ms Lanier said.