Donald Trump has not quelled fears about the impact of white supremacists on his new administration - despite disavowing the group earlier this week.

Critics have said the President-elect needed to take responsibility for the ongoing support from the "alt-right" movement which has associated itself with his white identity politics.

White nationalist leader Richard Spencer also agreed that Trump and the "alt-right" were "all riding in the same lane", and added that the billionaire businessman's shock election victory proved Spencer's view that "America must reject multiculturalism and "political correctness" in favour of its white, Christian heritage.

"Those groups clearly see something and hear something that causes them to believe he is one who sympathises with their voice and their view. Donald Trump has to take responsibility for that," said Representative Elijah Cummings of Maryland, a black Democrat, according to a report in the Associated Press.

Cummings was among 169 members of Congress who signed a letter opposing Stephen Bannon's appointment as Trump's chief strategist. Bannon, the former chief of Brietbart news, who also led Trump's media campaign, is known as a white nationalist, that "has built a political career out of demonising Muslims, immigrants, women, the LGBTQ community, and Jews".

But Trump told The New York Times that the allegations of anti-Semitism against Bannon and connections to the alt-right are "not him". "If I thought he was racist, or 'alt-right' ... I wouldn't even think about hiring him," Trump said on Tuesday.

On his own association with the far-right group, Trump told reporters:"I disavow the group. It's not a group I want to energise, and if they are energised, I want to look into it and find out why."

Following his surprise US election victory on November 8, there were public cries from the "alt-right" movement and Nazi-salutes, which Spencer said were just "ironic exuberance" that "the mainstream media doesn't get".

The Ku Klux Klan announced on its website plans to celebrate Trump's victory with a parade next month in North Carolina. "Trump's race united my people," the site declared.

Former Klan leader David Duke tweeted: "Make no mistake about it. Our people played a HUGE role in electing Trump!"