British Prime Minister Boris Johnson said the emotions triggered by the death of George Floyd in the US last month could not be ignored, and that his government must do more to fight prejudice towards people from black and minority ethnic groups.
The death of Floyd, an unarmed African-American man, has sparked protests around the world over police racism and brutality.
More than 100,000 people took part in antiracism protests around Britain at the weekend.
"We who lead and who govern simply can't ignore those feelings because in too many cases, I am afraid, they will be founded on a cold reality," Mr Johnson told The Voice, the UK's only black national newspaper.
He said UK had made great strides in tackling racism since the 1970s but it must also "frankly acknowledge that there is so much more to do in eradicating prejudice and creating opportunity".
Demonstrators defied warnings not to gather in large groups because of the risk of spreading the coronavirus.
Mr Johnson said that if such protests continued, the coronavirus epidemic might “get out of control”.
He said it was black and minority ethnic groups who had been at the forefront of the struggle against Covid-19 and had “paid a disproportionate price”.
A study by University College London this month revealed that the likelihood of death from Covid-19 was two or three times higher among England’s Black, Asian and minority ethnic groups than in the general population.
Otherwise peaceful demonstrations in London ended with small groups clashing with police. Dozens of police officers were injured and more than 100 people were arrested.
A statue of Winston Churchill in Parliament Square in London was sprayed with graffiti and in Bristol in western England, protesters toppled a statue of the 17th-century slave trader, Edward Colston.
"I will not support those who flout the rules on social distancing," Mr Johnson said.
"I will not support or indulge those who break the law or attack the police or desecrate public monuments."
He said those who attacked public property or officers would "face the full force of the law".
"They are hijacking a peaceful protest and undermining it in the eyes of many who might otherwise be sympathetic," Mr Johnson said.
"As a society, we can and must do better."
In the past, Mr Johnson has drawn criticism for comments he had made about foreigners.
In 2002, when he was a UK member of Parliament, he used the racist term “piccaninnies” to describe people in the Democratic Republic of Congo.
