Social media giant Facebook has rejected calls from both users and the Communications Minister to ban the dangerous practice.
Instead it has said that it is a platform for free sharing, and that controversial or offensive behaviour is not necessarily against its rules.
A Facebook spokesperson told independent.ie this evening: "At Facebook we try to be a platform where people can share freely whilst still protecting the rights of others.”
“We do not tolerate content which is directly harmful, for example bullying, but controversial or offensive behaviour is not necessarily against our rules.”
Minister for Children Frances Fitzgerald said earlier today that she had been in touch with Facebook on the issue, and it would remove the 'NekNomination' pages if online behaviour turns abusive.
"We've been in touch with Facebook and of course if any of this online behaviour becomes abusive or can be seen as bullying then clearly Facebook will take down the page.
"But much of this is interaction obviously between adults and really the information and education message has to get out there.
"This can be potentially lethal. It may have started off with what people thought was a fun thing but underlying it is really about abusive drink and our attitudes to alcohol," she said.
Facebook users have followed the lead of Communications Minister Pat Rabbitte in calling for a Facebook-wide ban of '#NekNomination' videos in order to stop the trend.
Many users have complained on Facebook pages about the fad, urging people to stop taking part.
One user reported to Independent.ie that Facebook refused to remove a 'NekNomination' page after he reported it using the site's reporting procedures.
The user, who has asked not to be named, reported the 'NekNomination' page for "self-harm" issues. Facebook responded to notify the user that they had not removed the page, a screenshot of which can be seen above.
Communications Minister Pat Rabbitte hit out at what he described as a "stupid and silly game" and warned about the "tragic consequences" associated with the social networking craze.
"Firstly the responsibility is with young people who are falling for a foolish and stupid rouse that can have devastating consequences," the minister said.
Mr Rabbitte said that it would be "helpful" if Facebook intervened, adding that he may ask an advisory council to examine the nek nomination phenomenon.
Meanwhile, a spokesperson for Google said it removes any videos which it believes to contravene its 'community guidelines'.
“All videos uploaded to YouTube must comply with our Community Guidelines,” the spokesperson said.
“The Guidelines prohibit ‘content that's intended to incite violence or encourage dangerous, illegal activities that have an inherent risk of serious physical harm or death’.”
“We also prohibit, among other things, videos that depict things drug abuse, and under-age drinking and smoking.”
“We count on our community members to know the Community Guidelines and to flag content they believe violates them. We review flagged videos quickly, and if we find that they do violate the Guidelines, we remove them."
A Facebook page called 'Ban Neknominations' was set up by Mary Carroll yesterday evening, and it has already gaining more than 15,000 likes.
She said she decided to take action after the deaths of two young people.
"It all really, really angered me. I reported the main Neknomination page to Facebook too, but they replied saying the page didn’t violate their community standards," she said.
"A lot of parents told me that they ddn't even hear of it until the weekend. Now that they know about it, they're confronting their teenagers about it and warning them of the dangers."
Meanwhile, some users have expressed their opposition to the trend in other ways.
Irish video examples include one man who sarcastically attempted to 'neck' a cup of tea, stopping after one sip because "I'm not hard enough". He then blasted the craze as 'stupid' and implored people to stop participating.
South African man Brent Lindeque "decided to create something positive" out of the trend. Instead of rapidly drinking a pint, he carried out an act of charity. His chosen charity act was to provide a man who was begging with a sandwich, chocolate bar and a bottle of coke. He then tagged two more people to carry out charity acts.
Linhdeque's video features facts and figures about poverty in South Africa overlaid on the screen as he carries out his anti-NekNomination.
He wants people to tweet their videos with the hashtag #OnlyTheGoodThings. He points out the power of the NekNomination craze and the difference that power could make if used for positive things.
"Downing a can of Castle Light is easy... imagine if we all harnessed the power of social media to make a real difference in peoples lives."