Thousands of US civil rights activists have kicked off a week of protests before Donald Trump's presidential inauguration with a march in Washington DC, vowing to keep fighting for equality and justice under the upcoming administration.

Chanting "no justice, no peace", protesters headed by the Reverend Al Sharpton marched on Saturday along the National Mall toward the Martin Luther King Jr Memorial, about three kilometres from the steps of the US Capitol where Trump will be sworn in as president on Friday.

Pre-march speakers denounced Trump to protesters, who braved drizzle and temperatures just above freezing to show their support for minority rights and President Barack Obama's signature of healthcare law, which the president-elect has vowed to dismantle.

"We stand together, not as a people of hate, but as a people of hope," said Charley Hames Jr, president of the Oakland, California chapter of Sharpton's National Action Network.

"We believe this march is the first of many."

Trump, a New York real estate developer, won with a populist platform that included promises to build a wall along the Mexican border and restrict immigration from Muslim countries.

He also promised to crack down on companies moving jobs out of the US.

Trump's disparaging comments about immigrants and women and his stance against Obama's healthcare law have drawn the anger of many on the left, who plan a series of protests.

"He's a clown," marcher Ken Coopwood Jr, 17, of Washington, told Reuters news agency. "I think he's not going to care about much, unless it's personal."

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Civil rights groups, including the National Association for the Advancement of Coloured People and the National Council of La Raza, as well as Democratic politicians, had all said they would take part in Saturday's march.

The protest began hours after Trump blasted US Representative John Lewis, a Georgia Democrat and civil rights campaigner, who had previously said he did not see the estate tycoon as a legitimate president.

Lewis told NBC News in an interview for Sunday's Meet the Press that he believed Russia's alleged hacking aimed at helping Trump put his legitimacy into question.

Trump replied on Twitter on Saturday that Lewis should focus instead on his Atlanta district. "All talk, talk, talk - no action or results! Sad!," he wrote.

About 30 groups, almost all of them anti-Trump, have obtained permits to protest before, during and after the inauguration.

Demonstrations throughout the week will voice support for women, healthcare, public education, anti-racism and peace, among other causes.

Thousands of demonstrators also have vowed to shut down the inauguration, including by closing off security checkpoints along the inaugural parade route.