First Minister Mark Drakeford has said the Black Lives Matter campaign is "fundamentally important" but he wished people had found other ways to protest rather than public demonstrations during the pandemic.
"There are other ways that don't pose a public health risk," he said.
Video showed a police officer kneeling on the unarmed black man's neck.
Further protests have been held in Wales on Sunday.
"I absolutely understand the strength of feeling that brings people to the sort of scenes we saw yesterday," Mr Drakeford told BBC Politics Wales.
"I'd wish they'd done it in a different way because I think there are other ways that don't pose a public health risk.
"But I do have to say to them again today, we are in the middle of a public health emergency."
Many protesters in Wales wore face coverings and others wore gloves.
"We're here to make a stand. We're here to show everyone's equal and, of course, black lives matter," one protester in Cardiff said.
The majority of Saturday's protests in the UK were peaceful but in the evening there were disturbances outside Downing Street.
Mr Drakeford added: "There were online protests going on yesterday, there are petitions running, there are organisations to join and campaign with.
"And I still say to people in Wales, please don't put yourself in a position where the strength of feeling, the absolute strength of feeling that I share on the Black Lives Matter issue leads you to do things that put yourself and other people at risk."
After seeing the large crowds in Cardiff, Andrew RT Davies, the former Conservative leader in the Senedd, said "lockdown and social distancing appears to be over in Wales".