There are claims that a number of foreign nationals are registered to vote in the abortion referendum.
Independent TD Mattie McGrath and Sinn Féin TD Peadar Toibin say they have been contacted by several people who did not even apply to vote.
Up to 125,000 extra people were added to the supplementary register in the last few months.
Pro-life TD Mattie McGrath wants an investigation into what has happened.
"What are you going to do about the register? I asked Minister Murphy, I wrote to him, I hand-delivered a letter today about the French student who were put on unknown to themselves and illegally on the register here in NUIG in Galway," said Minister McGrath.
The Taoiseach has said that the claims made by Mr McGrath are not true and told him to 'cool the conspiracy theories' about the electoral register.
"You can cool the conspiracy theory, Deputy McGrath," Mr Varadkar responded.
"The people who have voted so far are postal voters, although there is early voting on some islands and also some nursing homes - that is the norm.
"The allegation that a French student has been placed on the register, I understand that has been refuted."