Independent candidate Peter Casey has been criticised for comments made in a newspaper in which he said there were "freeloaders" in the direct provision system, who he said should be "put back on the plane".
During a debate on RTÉ's The Week in Politics, Mr Casey said that "genuine refugees" should be given a "warm Irish welcome" and ruled out joining up with Nigel Farage or any other right wing group if elected to the European Parliament.
Fianna Fáil candidate Brendan Smith said the comments attributed to Mr Casey in the Sunday Times were "terrible".
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He said: "People who are fleeing torture and horror and war are not freeloaders."
Mr Smith said Europe needs a migration policy to address the issues that are causing people to flee from their homelands.
Sinn Féin’s Matt Carthy said the treatment of asylum seekers in direct provision should be a source of shame to anyone in Fianna Fáil or Fine Gael.
"There are a lot of communities across our community who feel very frustrated and Peter is trying to tap into that by blaming foreigners," he said.
"It is not an accident that those newspapers that he got front page coverage of are London-based newspapers that promoted Brexit. They are playing political games," he added.
Mr Casey insisted he was not being used to promote a Brexit agenda.
He said: "Anyone who is coming from a war-torn area, we absolutely have a responsibility to take our allocation and we should.
"We should give them a passport, we should help them get work. We should look after them when they come in, we should not put them in jail with walls which is a direct provision camp.
"We should give them give them a warm /Irish welcome if they are genuine refugees."
He also said he supports "free movement within the EU, "but you can't have people coming into Ireland illegally and staying here and expecting to be housed and educated and looked after".
Fine Gael candidate Maria Walsh said: "Ireland is richer when we have immigrants."
Flanagan criticises EU's approach to Brexit talks
During the same debate, Independent Luke Ming Flanagan said he believes the EU has carried out its side of the Brexit negotiations in a "spiteful way".
He said Brexit was "potentially an opportunity to give a jolt to what is ever closer union". Such integration, he said, would mean Ireland "would lose the power to set its own tax rates"
The Roscommon-based MEP said Brexit is a far lesser threat to Ireland than that of an EU army. "Not money on guns, money on houses - that is what we needed," he said.
Asked if Brexit had made Sinn Fein less Eurosceptic, Matt Carthy said it has "allowed people to see the nuance of the Sinn Fein position: "We believe that Ireland's place is in the EU. But we also believe EU needs to be radically reformed."
Mr Smith said Ireland needs MEPs who would work to limit the damage of Brexit because it is negative for our country regardless what arrangement Britain leaves with.
Asked whether he still supports the idea of an Irish exit from the EU, Mr Casey said he has changed his mind on that.
Asked if he still wants to take Ireland out of the Euro, Mr Casey said he doesn't. "I floated that suggestion and I was told we can't leave the Euro and stay in the EU so the answer to that is no," he said.