The LoveBoth campaign has called on the Government to ask Google to ban websites which allow people to import abortion pills.
The group, which is advocating a No vote in the forthcoming referendum, said restrictions should be placed on the ability of internet providers to target women advertising abortion pills.
It also called for the Government to launch a campaign to highlight the dangers of abortion pills and “resourcing the customs authorities to intercept them”.
Spokeswoman and legal advisor Caroline Simons said: "What we are proposing is quite plausible. You hear people complaining about the drinks industry being allowed to fund sporting events and there is a health issue and concern there.
"We are not talking about banning websites as such. We are simply talking about restricting abortion pills in Ireland. "
Ms Simons said the Minister for Health Simon Harris had "used" the two masters of the maternity hospitals Dr Rhona Mahony and Professor Fergal Malone to "win votes".
The doctors had attended an event on Monday with Mr Harris calling for a Yes vote in the referendum on the Eighth Amendment, which protects the equal right to life of the mother and the unborn, on Friday.
The campaign group was questioned about whether a woman should face 14 years in prison if she procures an abortion. Ms Simons declined to answer insisting this was a matter to be dealt with after the result on Friday.
“I am looking at all the distractions the Government are putting in front of the voters. The only thing the voters need to know by Friday is that in the absence of any evidence that is medically necessary to address a health issue or the threat to a woman’s life, we are being asked to remove all Constitutional protections from unborn babies.”
