Labour Senator Lorraine Higgins' Private Members' bill on internet safety has passed the second stage in the Seanad, with 22 Senators voting in favour and four opposing it.
Introducing the bill, Ms Higgins said: "While much online abuse targeted at teenagers and politicians has been well documented in the past, in recent days focus has returned to this issue with Meath footballer Paddy O’Rourke being threatened and told - 'Don't think I won't knife you brother' on twitter."
She said having "a legislative vacuum in this area is nothing short of a failure on the part of legislators in this country".
Her bill contains a section stating electronic communications shall be considered harmful if they incite or encourage another to commit suicide, cause serious harm to themselves, or include explicit content of the other as is the case with revenge porn.
Fianna Fáil Senator Thomas Byrne said the area of internet safety is a tricky area and there is no doubt some laws need to be updated.
He said his party would support Senator Higgins' bill, but there would have to be significant changes to it.
Mr Byrne said: "I certainly believe there should be an exemption for the expression of political views. If it was personalised, that is totally different."
Minister for Justice Frances Fitzgerald said the Law Reform Commission is currently carrying out a project on cyber-crime at the moment.
She said the Government is not opposing the bill at this stage.
Meanwhile, Independent Senator John Crown is opposing the bill. He said free speech is the cornerstone of any democratic society.
He added "the wonderful Maíria Cahill widely used the medium and she caused quite a bit of alarm, distress and harm to people who deserved it and it was done deliberately. This bill would have allowed people who were on the receiving end of valid criticism ... to hide behind it."