A statue of Christopher Columbus in Boston has been beheaded, police said Wednesday, as calls to remove sculptures commemorating colonisers and slavers sweep America on the back of anti-racism protests.

A Columbus statue was also vandalised in downtown Miami, and another was dragged into a lake earlier in the week in Richmond, Virginia, according to local reports.

The incidents come as pressure builds in the United States to rid the country of monuments associated with racism following massive demonstrations over the killing of George Floyd by a white police officer in Minneapolis last month.

Italian explorer Columbus, long hailed by school textbooks as the so-called discoverer of "The New World," is considered by many to have spurred years of genocide against indigenous groups in the Americas.

He is regularly denounced in a similar way to Civil War generals of the pro-slavery South.

The Boston statue -- which stands on a plinth in the heart of town -- has been controversial for years, like other Columbus statues across the US, and has been vandalised in the past.

Boston police were alerted to the damage shortly after midnight on Tuesday, a spokesman told AFP. An investigation is under way but no one has been arrested, he added.

A jogger running past the statue Wednesday said she approved of the decapitation.

"Coming out of the Black Lives Matter protests, I think it's a good thing to capitalise on this momentum," she told AFP, without giving her name.

"Just like black people in this country, indigenous people have also been wronged. I think this movement is pretty powerful and this is very symbolic," she added.

Dozens of American cities have over the years replaced "Columbus Day" in October — which became a federal holiday in 1937 — with a day of tribute to indigenous peoples.

But not Boston or New York, which have large Italian-origin communities.

Boston's mayor Marty Walsh condemned the beheading but added that the statue would be removed on Wednesday pending a decision about its future, local media reported.

Protesters also defaced a Miami statue of Columbus at a waterfront park with red paint and messages that read "Our streets," "Black Lives Matter" and "George Floyd," before police made several arrests, according to the Miami Herald newspaper.

In Virginia, protesters used ropes to pull down the eight-foot (2.44-meter) statue and then dumped it in a nearby lake Tuesday, the Richmond Times-Dispatch said.

It echoed an incident in Bristol, England, on Sunday when demonstrators toppled a statue of a slave trader and dumped it in a harbour during anti-racism protests.