Those who vandalise or take down referendum posters should be pursued by the gardaí, Fianna Fáil believe.
Fianna Fáil TDs Willie O'Dea and Mary Butler have come out to "condemn unreservedly" the tearing down of posters.
It comes as a number of complaints have been made, including one from former Education Minister Jan O'Sullivan who reported the pulling down of Labour party referendum posters in Limerick city to gardaí.
Speaking outside Leinster House this morning, Mr O'Dea said: "I have had experience in the past of my own posters being taken down and it's very frustrating, very annoying because as you know posters are pretty expensive, people are entitled to put up posters that's the system we have.
"Anybody who takes down posters whether they be for the yes side or the no side should be pursued.
"It is an activity which I condemn unreservedly," the Limerick TD said.
This was echoed by Waterford TD Ms Butler who said: "We have called for a respectful debate whether you are on the yes side or the No side."
She said she had seen a "huge No poster" torn down on the way to Dungarvan over the weekend.
"They cost a lot of money to put up.
"The tearing down of posters whether they are Yes or No is obviously not the right way to deal with this issue, people are entitled to put up their posters," she said.
While Ms Butler said she will be actively campaigning for a No vote, Mr O'Dea will not be getting involved in the referendum campaign.
"I did say that I wouldn't be campaigning one way or the other and I think people appreciate that."
He said signs have been put on many doors in Limerick which say "no referendum campaigning".
"Most of my constituents would prefer if politicians stood back from the matter and allowed people make up their own minds."