Police in Bristol made two arrests yesterday, after around 300 people attended a demo.
They say there were a few incidents of minor disorder, but it was largely peaceful.
Some people gathered at the city's cenotaph for what some of those attending called an 'all lives matter protest'.
It followed a 'black lives matter' protest last weekend, which saw a statue of slave trader Edward Colston being toppled.
In London police yesterday arrested more than 100 people after a demo turned violent with six police officers suffering minor injuries.
Thousands defied a ban on mass gatherings to protest in the capital - many of them thought to be connected to far-right groups.
Boris Johnson says "racist thuggery has no place on our streets", Home Secretary Priti Patel said it was "appalling".
The chief constable of Wiltshire Police called it pure thuggery. Keir Pritchard says there's no place for violence towards officers.
Scotland Yard has launched an investigation after a photo emerged of a man urinating next to the memorial to PC Keith Palmer, who was murdered during Westminster terror attack.
It apparently happened during yesterday's protests in Parliament Square.
Labour leader Sir Keir Starmer has described it as "beneath contempt".
Tory MP Tobias Ellwood, who tried to save PC Palmer's life in 2017, says it's "abhorrent".
There are Black Lives Matter rallies planned today in Leeds, High Wycombe and south London.
Around 300 people attended a demo in Bristol city centre today. Our priority has been to maintain public safety at all times & had an appropriate plan in place. It was largely peaceful, with a few incidents of minor disorder & 2 arrests. The majority of the group have dispersed.— Avon and Somerset Police (@ASPolice) June 13, 2020