US military leaders have been denouncing racism and intolerance since a white supremacist rally in Virginia -- with condemnation mounting after President Donald Trump said counter-protesters also were to blame for the violence.

The military usually stays out of the political fray, but it has been especially keen to distance itself from the weekend's neo-Nazi demonstrations because some demonstrators were sporting US military clothes or insignia.

In comments that were warmly embraced by David Duke, a former "grand wizard" of the Ku Klux Klan, Trump on Tuesday said the "alt-left" was partly responsible for the deadly violence in Charlottesville, and said there were "very fine people on both sides" of the protest.

On Wednesday General Mark Milley, who is chief of staff of the Army, took to Twitter to reinforce his service's values.

"The Army doesn't tolerate racism, extremism, or hatred in our ranks. It's against our Values and everything we've stood for since 1775," Milley wrote.

Marine Commandant General Robert Neller also sent a message after Trump's comments.

"No place for racial hatred or extremism in @USMC. Our core values of Honor, Courage, and Commitment frame the way Marines live and act," he wrote.

Admiral John Richardson, who heads the Navy, had issued a statement Saturday calling the events in Charlottesville "shameful."

"The Navy will forever stand against intolerance and hatred," he said.

Air Force Chief of Staff General David Goldfein later tweeted a message saying he supported his fellow military leaders.

"I stand with my fellow service chiefs in saying we're always stronger together-it's who we are as #Airmen," Goldfein wrote.

And Pentagon chief Jim Mattis on Monday said he was "very saddened" by what had happened in Charlottesville.

Images of Swastika-waving neo-Nazis circulated globally from the protests.

One man, who was photographed making a Nazi salute, wore a baseball cap bearing the logo of the 82nd Airborne Division.

The legendary military unit was quick to distance itself from any association with the man.

"Our WWII Airborne forefathers jumped into Europe to defeat Nazism. We know who we are. We know our legacy," the 82nd wrote on Twitter, creating a chain of comments in which the relatives of those who fought in World War II posted photographs or the gravestones of loved ones who battled Nazis.