Keir Starmer has said Britain will "never surrender" its flag to those who use it to sow "violence, fear and division".
The Prime Minister said the flag represents "our diverse country" and he would not tolerate people being intimidated on the streets due to their background or the colour of their skin.
It comes after between 110,000 and 150,000 people attended what is thought to be the largest nationalist demonstration in decades, organised by far-right agitator Tommy Robinson.
Tech billionaire Elon Musk has been condemned for telling the crowds in London on Saturday that "violence is coming" and “you either fight back or you die”.
In his first comments since the march, Mr Starmer said: "People have a right to peaceful protest. It is core to our country's values. But we will not stand for assaults on police officers doing their job or for people feeling intimidated on our streets because of their background or the colour of their skin.
"Britain is a nation proudly built on tolerance, diversity and respect. Our flag represents our diverse country and we will never surrender it to those that use it as a symbol of violence, fear and division."
Twenty-four people were arrested and 26 police officers were injured, including four who were seriously hurt, at the event in London, according to the Metropolitan Police.
People were arrested for a range of offences including affray, violent disorder, assault and criminal damage.
Earlier, Business Secretary Peter Kyle criticised Mr Musk for his comments, which included a call for the dissolution of Parliament.
He said: "I thought that they were slightly incomprehensible comments that were totally inappropriate. But what we saw yesterday was over 100,000 people who were expressing freedom of association, freedom of speech, and proving that both of those things are alive and well in this country.
"A small minority of people who are protesting committed acts of violence against our police for which they should and they will be held accountable."
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Mr Kyle said Robinson was stoking anger by tapping into a wider "sense of disquiet" and said the Government was working to bring communities back together.
He said: "There are communities that are being driven further apart, and there are figures such as Tommy Robinson that is able to touch into a sense of disquiet and grievance in the community in our society.
"A lot of it goes back to its roots in the financial crisis and the impact that had on communities around the country, and we haven't been able to bring our communities back together again since.
"I think these are moments that are klaxon calls to us in public life to redouble our efforts to address the big concerns that people right across our country have, and immigration is a big concern."
Liberal Democrat leader Ed Davey said: “Elon Musk openly called for violence on our streets yesterday.
“I hope politicians from all parties come together to condemn his deeply dangerous and irresponsible rhetoric. Britain must stand united against this clear attempt to undermine our democracy.”