There are calls for Gardaí to enforce hate speech legislation and social media companies to do more to combat racism.
It follows a rally yesterday during which Gardaí had to keep two rival groups of protestors outside Google's Dublin headquarters apart.
A group of anti-racism campaigners were holding a rally demanding stronger action.
Among the speakers at the anti-racism rally was Green Party Councillor Hazel Chu, who detailed how she has been targeted.
Got more mail than ever. Great mix of lovely & some rather hate fill ones.
Spoke to Gardai on hate mail & six breathing calls I got. They're going to perform trace.
Acted as Lord Mayor.
Got constituency work done.
"There was an attempt to hack into my Twitter account and following that there was a petition set up to ask me to resign," said Cllr Chu.
"Then, a day later, I started to receive phone calls.
"The first was a phone call with just some heavy breathing and then following up from that there was about five more phone calls in one day."
Addressing yesterday's rally, Ms Chu said: "Someone from abroad with a lot of following tweeted at my name questioning whether I was from Ireland, saying that I clearly wasn't and that I was just pretending to be Irish and then tweeting those kind of things.
"That kind of snowballed then because all of a sudden instead of a handful of messages coming my way that were questioning my nationality and ethnicity, suddenly it was hundreds."