Taoiseach Enda Kenny has urged young people not to partake in internet drinking activities such as Neknomination.
It involves people being nominated to drink large amounts of alcohol and post a video online,
Speaking in Galway, Mr Kenny said it was not a game and young people should give it up.
The Taoiseach said Neknomination offered no personal challenge of any benefit and had the most horrific consequences, which could end lives.
Neknomination has been linked to the death of Jonny Byrne from Leighlinbridge in Co Carlow.
The body of the 19-year-old was taken from the River Barrow yesterday morning.
Minister for Communications Pat Rabbitte earlier said "it would be helpful if Facebook agreed to take down" Neknominate pages.
Speaking this morning, Mr Rabbitte said the Internet Content Governance Advisory Group may be prepared to look at the "stupid and silly phenomenon".
However, he said the "first responsibility is with the young people who are falling for a stupid ruse".
He encouraged people to have regard for a campaign by the Union of Students in Ireland against the drinking game.
Facebook said controversial or offensive behaviour is not necessarily against its rules.
A spokesperson said: "We encourage people to report things to us which they feel break our rules so we can review and take action on a case by case basis.
"We also give people the ability to remove themselves from an uncomfortable conversation through tools such as untagging and blocking."
Meanwhile, a senior criminal judge has warned that if internet drinking contests continue, they will result in a "tsunami" of homicide and rape prosecutions before his court.
Mr Justice Paul Carney was speaking as he was sentencing a 38-year-old Waterford man who, after drinking six to seven pints of lager, raped an acquaintance having offered her a lift home from their local nightclub.
He said it was the latest case in a long line in which young men with no previous convictions and from good families take a quantity of drink they are not used to and "end up the following morning facing responsibility for a homicide or a rape and it seems to be a lottery as to which it is going to be".
"It's a male phenomenon," he continued before adding: "If the current internet drinking contest takes hold, it is going to result in a tsunami of homicide and rape prosecutions coming before this court".
Union of Students issues warning
USI President Joe O'Connor also warned young people of the dangers in taking part in Neknomination.
Speaking on RTÉ's Morning Ireland, Mr O'Connor urged people who are involved in the game to be aware of the impact it may be having on children or vulnerable people.
"One of the big dangers that we're seeing associated with this is not just the impact on the individual or the group taking part but on younger children who may be on social media; vulnerable people who wouldn't normally find themselves in this situation.
"We're asking people to think about the impact or influence it may have on them, particularly as a result of the tragic events we've seen in the last 48 hours.
"There's a huge amount of peer pressure involved. It can lead to cyberbullying and online shaming of people who do not take part and that's certainly been a factor as to why it has escalated."
Elsewhere, consultant gastroenterologist at Beaumont Hospital Professor Frank Murray said more people will die if the phenomenon continues.
Speaking on RTÉ's News At One, Professor Murray, who is chairman of the Royal College of Physicians Policy Group on Alcohol, called for urgent measures to restrict the availability of cheap alcohol.
"It is very cheap, it is very affordable, and it is available in a very widespread way. We would support that rapid introduction of minimum unit pricing.
"There has been a five-fold increase in the number of off-licences in the south of Ireland, that is ridiculous. Petrol stations are selling alcohol, almost all convenience stores, and we think that it should be available in a more regulated way and in fewer outlets."