Boris Johnson does not think Britain is a racist country, the prime minister's spokesman has said.
"The PM doesn't doubt that there continues to be discrimination and racism but does not agree that this is a racist country," the spokesman said.
"We have made very significant progress on this issue but there remains more to do and we will not be complacent in our efforts to stamp out racism and discrimination where it happens."
Thousands of people have taken to the streets in recent days in the wake of the killing of George Floyd in police custody in the US.
While the protesters here have voiced their anger at the killing of Mr Floyd, they have also sought to highlight issues faced by black people in the UK and call for action to tackle racial injustice.
Thousands turned out at locations across the UK for the demonstrations at the weekend, despite warnings for people not to gather during the coronavirus pandemic.
In Bristol, the city's statue of slave trader Edward Colston was torn down and thrown into the harbour by protesters.
The protests in the city were attended by an estimated 10,000 people and there were no arrests, police said.
Downing Street said the removal of the statue was "criminal act".
But Mr Johnson's spokesman did not answer directly when asked if it was right that there were still statues of figures involved in the slave trade in public spaces.
"The PM's view is that in this country, where there is strong opinion, there is a democratic process which should be followed," he said.
"People can campaign for the removal of a statue but what happened yesterday was a criminal act and when the criminal law is broken that is unacceptable and the police will want to hold to account those responsible."
The spokesman added: "The PM absolutely understands the strength of feeling, but in this country we settle our differences democratically and if people wanted the removal of the statue there are democratic routes which can be followed."
As well as the statue being toppled in Bristol, some protesters in London clashed with the police and graffiti was scrawled on the statue of Sir Winston Churchill in Parliament Square.
This prompted the PM to say that the anti-racism protests had been "subverted by thuggery" that betrays their cause.
The Metropolitan Police said 36 people were arrested on Sunday for offences including violent disorder, criminal damage and assaulting police.
They added that 35 officers reported suffering injuries, with two needing hospital treatment.
One suffered a head wound, while other sustained a shoulder injury after being hit by a thrown bottle.
On Saturday, 29 people were arrested and 14 officers injured in the capital.