White supremacists have welcomed US President Donald Trump's insistence on blaming "both sides" for the deadly violence in Charlottesville, Virginia last weekend.

The praise for the Republican leader, however, drew concern and condemnation from across the political spectrum, including from senior figures from within his party.

On Wednesday, Trump was forced to disband two business advisory councils, after he was pressured by corporate leaders over his response to the weekend protests that killed at least one person.

Trump made the decision after another executive, 3M Co's Inge Thulin, became the latest member to leave his American Manufacturing Council, and the Strategic and Policy Forum broke up of its own will.

OPINION: Charlottesville is America everywhere

"Rather than putting pressure on the businesspeople of the Manufacturing Council & Strategy & Policy Forum, I am ending both," Trump wrote on Twitter.

Tensions are high after a white supremacist mowed down a crowd of anti-racists on August 12 in Charlottesville, killing anti-fascist protester, Heather Heyer, and injuring dozens - some severely

Trump initially blamed "many sides" for the violence and avoided calling out the far-right by name.

After an outcry, he specifically condemned white supremacy two days later.

But by Tuesday, Trump again criticised "both sides" including anti-fascist protesters, who he described as the "alt-left", a term popularised by white supremacists groups.

The US president referred to "very fine people" on both sides of the divide.

Reacting to Trump's latest statement, Andrew Anglin, administrator of now defunct neo-Nazi blog the Daily Stormer, praised Trump's reaction with the anti-Semitic headline: "Trump Finally Gives Half-Assed Charlottesville Statement to Whining Jew Media".

"I knew Trump was eventually going to be like meh, whatever," Anglin wrote. "Trump only disavowed us at the point of a Jewish weapon. So I'm not disavowing him."

Others also read Trump's reaction as made out of political expedience rather than genuine ill-feeling.

Neo-Nazis on Twitter and the 4Chan forum celebrated what they saw as a coded message of support from Trump.

Right-wing leader Richard Spencer and former KKK leader David Duke also lavished praise on Trump.

Duke wrote on the social media platform: "Thank you President Trump for your honesty and courage to tell the truth about Charlottesville and condemn the leftist terrorists in BLM/Antifa".

Black Lives Matter (BLM) is a US-based civil liberties organisation demanding equal rights for African Americans and an end to police brutality.

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Condemnation against Trump were also swift.

Activist and writer Shaun King said Trump's speech on Tuesday was an "an open embrace of white supremacy".

"As expected, white supremacists loved the off-script press conference Donald Trump just gave. Loved it."

Senior Democrat and senate minority leader, Chuck Schumer, said Trump's purported neutrality was indicative of his sympathies.

By saying he is not taking sides, Donald Trump clearly is. When David Duke and white supremacists cheer, you’re doing it very very wrong Chuck Schumer, Democrat senator

"By saying he is not taking sides, Donald Trump clearly is. When David Duke and white supremacists cheer, you're doing it very very wrong," he tweeted.

Al Franken, another Democratic senator, who is of Jewish faith, also posted on social media.

When someone shows you who they are, you believe them. Trump is again letting white supremacists off the hook for #Charlottesville violence. — Sen. Al Franken (@SenFranken) August 15, 2017

Trump's presidential campaign last year enjoyed broad far-right backing, and the Trump administration includes several figures linked to far-right and neo-Nazi groups.

During the campaign, the Trump team had targeted minority groups, including immigrants from Latin America, refugees, and Muslims

The president, a former reality TV star, has described immigrants from Mexico as "drug dealers, criminals, rapists" and called for a complete shutdown of Muslims entering the US.

A watered down version of his Muslim ban was later introduced, only to be rejected by courts.