The Garda Commissioner Drew Harris has said officers are identifying suspects involved in online abuse directed at a family, who have been forced to leave Ireland after receiving a death threat.
It comes after a TD slammed online platforms over their handling of online harassment.
The Ryan family were targeted with a series of racially-abusive messages after taking part in a recent supermarket ad.
Fiona Ryan, her partner Jonathan, who was born in Brazil, and their son Jonah are moving to England as they fear for their safety after receiving a series of racially abusive messages and death threats after appearing in a Lidl advert.
Fianna Fáil's Jack Chambers brought up the Ryan family at the Oireachtas Justice Committee where Facebook, Google and Twitter are being grilled by TDs and Senators today.
He said removing the offensive tweets was "weak" and asked Karen White from Twitter about it.
Mr Chambers asked: "If someone with a huge amount of followers brings hatred to a big audience that promotes a racist message to a huge audience, does a simple deletion of that rectify and remedy the consequences for a person who feels they have to leave the country?"
Ms White said: "I would sympathise with anyone who has been subjected to targeted abuse or harassment of violent threats whether it's online or offline. It's abhorrent and unacceptable.
"I want to reassure the committee that we have very robust policies in place in Twitter around hateful behaviour and hateful conduct and violent threats when we are made aware there is a range of enforcement actions we can take."
She added that "simply removing content from a service is not in all instances going to change the intolerance".
Ms White said: "There is a purpose there in trying to educate that particular user that they have broken the rules.
"Consistent rule violations will result in permanent suspension."
Mr Chambers replied: "Your net response is to broaden the fudge, that seems to be your public policy response to a lot of issues: It is complicated, it is multinational, we are platforms not publishers.
"I think when you bring it down to the family that was affected on your platform, the response from Twitter was to delete the tweet and that was it. Surely your enforcement mechanisms can be improved."
At the Gardaí's new Diversity and Integration Strategy, Commissioner Harris said officers are investigating.
He said: "We remain in contact with the Ryan family and we are now in the process of identifying individuals we believe are suspects in terms of offences that may have been committed.
"Then we will go through a process of interviewing them, gathering evidence and reporting that matter then to the DPP."
The three-year strategy includes improved ways of reporting, with members undergoing specific diversity and hate crime training.
However, the Garda Commissioner said specific hate crime legislation would help.
The Commissioner said: "Undoubtedly hate crime being recognised in terms of the very corrosive effect it has on victims should have a legislative basis, and we would support that."
The Garda's new definition of hate crime is "any criminal offence which is perceived by the victim or any other person to, in whole or in part, be motivated by hostility or prejudice, based on actual or perceived age, disability, race, colour, nationality, ethnicity, religion, sexual orientation or gender”.
