The Lord Mayor of Dublin, Tom Brabazon, is urging people to sign an online book of condolence for George Floyd rather than protesting.
Thousands of people attended a Black Lives Matter demonstration in Dublin on Monday with another planned tomorrow.
The online book of condolence can be found here.
Meanwhile, organisers of separate events in Cork and Galway have postponed their demonstrations.
A memorial service was held in the US last night for Mr Floyd who died after a police officer knelt on his neck.
I have opened an online Book of Condolence so Dubliners can express their sympathy to the family of George Floyd RIP and to give their support those who fight racial injustice worldwide. It can be signed at https://t.co/1gWQWbwZMz until 17th June. pic.twitter.com/Ei7FTaVfdb— Lord Mayor of Dublin (@LordMayorDublin) June 3, 2020
Councillor Tom Brabazon said people should not be attending mass gatherings.
Cllr Brabazon said: "I understand why people were angry, I understand why people felt the need to protest but we are in the middle of a pandemic and I would urge people to look at alternatives in terms of getting the message across.
"One of those ways is the online book of condolences that was opened up by Dublin City Council.
"The organisers won't have control over every individual and while a lot of the individuals will try to be responsible and try and socially distance, it's not always going to be possible with the numbers involved.
"They really need to take a second look at having this protest and look at alternatives. I would plead to them to do so."