Two senior US military officers have made what has been interpreted as veiled criticism of Donald Trump in the wake of his comments about the Nazi-led violence in Charlottesville.

Mark A Milley, the US Army Chief of Staff, said in a tweet the army did not accept “racism, extremism and hatred”, though he did not specifically condemn the President, or even mention him.

In the tweet, Mr Milley said: “The Army doesn’t tolerate racism, extremism, or hatred in our rank. It’s against our values and everything we’ve stood for since 1775.”

Another senior officer, General Robert B Neller, Commandant of the United States Marine Corps, also appeared to counter Mr Trump’s comments. “No place for racial hatred or extremism in @USMC. Our core values of Honour, Courage, and Commitment frame the way Marines live and act,” he said on Twitter.

Mr Trump has faced widespread criticism since he veered off the teleprompter at an infrastructure press launch and began answering questions as to whether or not he had been slow to denounce white supremacist-led violence that resulted in the death of one young woman, Heather Heyer, and the injury of up to 20 others over the weekend.

Mr Trump had initially sought to say there had been wrong on “all sides”, but under intense pressure from within his own party and without, he then issued a statement in which he said racism was evil and denounced white supremacy and neo-Nazism.

But as he was questioned on Tuesday afternoon about his slow-paced response to the incident, Mr Trump became defensive and then went on the attack.

White House Chief of Staff John Kelly watches on nervously at Trump's Charlottesville press briefing

“You had a group on one side that was bad and you had a group on the other side that was also very violent,” he said. “I thought what happened was a horrible moment for our country, but there are two sides to every story.”

Many public figures and officials have come out to condemn the violence at the white supremacists' rally in the Virginia college town, including senior member of the Republican Party. There have been mounting calls for the President to fire a number of his White House staff, among them Steve Bannon, who have been accused of promoting nationalism or white nationalism. Mr Trump notedly refused to voice his support for Mr Bannon when he was asked at the same press conference.

Violence on the streets of Charlottesville Show all 9 1 /9 Violence on the streets of Charlottesville Violence on the streets of Charlottesville Protesters clash and several are injured White nationalist demonstrators clash with counter demonstrators at the entrance to Lee Park in Charlottesville, Virginia. A state of emergency is declared, August 12 2017 Violence on the streets of Charlottesville Trump supporters at the protest A white nationalist demonstrator walks into Lee Park in Charlottesville, Va., Saturday, Aug. 12, 2017. Hundreds of people chanted, threw punches, hurled water bottles and unleashed chemical sprays on each other Saturday after violence erupted at a white nationalist rally in Virginia. AP Photo Violence on the streets of Charlottesville State police stand ready in riot gear Virginia State Police cordon off an area around the site where a car ran into a group of protesters after a white nationalist rally in Charlottesville, Virginia AP Photo Violence on the streets of Charlottesville Militia armed with assault rifles White nationalists, neo-Nazis and members of the 'alt-right' with body armor and combat weapons evacuate comrades who were pepper sprayed after the 'Unite the Right' rally was declared a unlawful gathering by Virginia State Police. Militia members marched through the city earlier in the day, armed with assault rifles. Getty Images Violence on the streets of Charlottesville Statue of Confederate General Robert E Lee The statue of Confederate General Robert E. Lee stands behind a crowd of hundreds of white nationalists, neo-Nazis and members of the 'alt-right' during the 'Unite the Right' rally 12 August 2017 in Charlottesville, Virginia. They are protesting the removal of the statue from Emancipation Park in the city. Getty Images Violence on the streets of Charlottesville Racial tensions sparked the violence White nationalists, neo-Nazis and members of the 'alt-right' exchange insults with counter-protesters as they attempt to guard the entrance to Lee Park during the 'Unite the Right' rally Getty Violence on the streets of Charlottesville A car plows through protesters A vehicle drives into a group of protesters demonstrating against a white nationalist rally in Charlottesville, Virginia. The incident resulted in multiple injuries, some life-threatening, and one death. AP Photo Violence on the streets of Charlottesville Rescue personnel help injured people after a car ran into a large group of protesters after an white nationalist rally in Charlottesville, Virginia AP Photo Violence on the streets of Charlottesville President Donald Trump speaks about the ongoing situation in Charlottesville, Virginia from his golf club in Bedminster, New Jersey. He spoke about "loyalty" and "healing wounds" left by decades of racism.

This is not the first time that Mr Milley has appeared to stand up to some of Mr Trump’s more controversial comments or directives. Last month, when Mr Trump tweeted that transgender people could not serve in the armed forces, Mr Milley was among those within the military hierarchy that said it would not act on the announcement until it received a formal directive from the White House.