The Minister for Transport has said that drafting difficulties in relation to the definition of the use of mobile devices in cars lead him to temporarily shelve the issue.
Paschal Donohoe said he made the decision to allow other important road traffic legislation pass through the Oireachtas.
The minister said he was concerned that if he had pursued the matter it would have delayed the implementation of everything else, including provisions for deal with drink driving.
Plans to restrict the use of smartphone messaging apps while driving have been withdrawn from new road traffic legislation.
The Government had planned to eliminate all texting and accessing the internet while driving, but decided to withdraw the provisions because of time constraints ahead of the general election.
Plans to restrict use of smartphone apps & social media while driving now withdrawn from new traffic legislation https://t.co/z7psoQSOAR— RTÉ News (@rtenews) January 18, 2016
When the Heads of the new Road Traffic Bill were published last year they included a provision to ban the use of smartphone messaging apps such as Whatsapp, Facebook or Viber while driving.
It is already an offence for motorists to send standard SMS text messages, or to hold a mobile phone while driving, but the Department of Transport had proposed to update the law to deal with more modern methods of communication.
The new road safety legislation will focus on the areas of drug driving, mutual recognition of driver disqualification with the UK and the introduction of a 20km speed limit in certain areas.
Mr Donohoe said that it was already an offence to hold a mobile phone while driving and to use a device that sits in a cradle and between January and October last year over 23,000 fixed charge notices were served.
Speaking on RTÉ's News at One, he said an increasing number of cars have mobile screens built into them, which can be used in various ways and the challenge was in how that usage could be defined.
Mr Donohoe said he wanted to be to be confident that legislation could not be challenged.
He said: "What would be real failure is to go ahead with a law that I knowingly judged to have a risk of clear failure. That would be wrong. It would put at risk the kind of enforcement measures that our gardaí are involved with.
"It would pose further challenge to the credibility of road traffic law. I'm not going to go down that route."
The founder of road safety group Public Against Road Carnage has said she is not surprised that plans to restrict the use of smartphone messaging apps while driving were withdrawn.
Speaking on RTÉ's Morning Ireland, Susan Gray said the move would have been "totally unenforceable for the gardaí."
Ms Gray said under the current legislation, gardaí must see a person holding a mobile phone while driving, to be able to prosecute.
She said they could never prove if someone was actually texting on a hands-free kit.
She said members of her organisation met Minister Donohoe to express their concerns over the proposed extension of the legislation, as they knew gardaí could not enforce it.
She said they would like to see greater resources given to gardaí in terms of enforcing policies of the current offence, which is holding mobile phone while driving
She also said when people are convicted in court of using a mobile phone while driving, they should get five penalty points, something she said is "not always happening".