"One of the founding principles of the EU is the free movement of people, we respect that absolutely and completely," said Enda Kenny, a practicing Catholic.
"That movement has to be irrespective of colour or creed, I disagree with the emphasis that Viktor Orban has put on that," added Mr Kenny.
Ireland is to take in at least 1,800 refugees amid growing public outcry over the tens of thousands of people fleeing to Europe's borders.
The country's response effectively trebled original plans announced in July to accept 600 refugees, mainly from Syria and Eritrea, over the next two years.
Prime Minister David Cameron has also said he will set out plans next week for the UK to take "thousands more" refugees from camps on the Syrian borders.
A petition calling for the Government to accept more asylum seekers has gained more than 300,000 signatures - three times the number required for the matter to be considered for a debate in Parliament.
The petition states: "There is a global refugee crisis. The UK is not offering proportional asylum in comparison with European counterparts.
"We can't allow refugees who have risked their lives to escape horrendous conflict and violence to be left living in dire, unsafe and inhumane conditions in Europe. We must help."
Ireland's Justice Minister Frances Fitzgerald revealed her country's increase two days after images emerged of three-year-old Syria Aylan Kurdi's body being washed up on a Turkish beach, accepting government ministers failed to keep up with the public outcry.
"What we have seen is heartbreaking and tragic and I think it demands the most comprehensive response," she said.
"I think it will be in the thousands. It's very hard to put a precise figure on it. We want to respond in as humanitarian a way as possible."
Ms Fitzgerald said if European leaders agree to increase the number of refugees being accepted across the bloc to 150,000, it will effectively treble Ireland's commitment to the crisis.
"I believe that is a minimum of the response that we will be making," she told RTE Radio.
Ms Fitzgerald said Ireland and Europe's response should not only be about opening borders to refugees and migrants but also ongoing aid programmes, the naval search and rescue operation which has been extended into the autumn.
She said work was also needed in the countries of origin and more efforts were needed to interrupt people traffickers.
Separately, it is expected 3,500 to 4,000 people will seek asylum in Ireland this year, a country with a population of 4.5 million and an economy growing faster than the rest of Europe after several years of recession and austerity.
The Irish Government made the announcement as the United Nations high commissioner called for Europe to draw up a common mass relocation plan for 200,000 refugees - the worst crisis of its kind since World War Two.
Germany has already accepted 35,000 vulnerable Syrians through a UN refugee scheme, Canada more than 10,000, Australia 5,600 and Switzerland 3,500.
Germany also expects to take in a total of 800,000 asylum seekers through all routes this year.
