Simon Coveney said the Government recognises the fact that most Irish people wanted the State to respond to the crisis in a compassionate way.
“And that’s what we are going to do,” he insisted.
Final decisions on exact numbers will not be taken until a crisis meeting of EU leaders on September 14.
But he said the Cabinet had already given Justice Minister Frances Fitzgerald a mandate to increase the figure from 600 before the distressing images of drowned Syrian toddler Aylan Kurdi emerged during the week.
With reports that EU countries will be asked to relocate 150,000 refugees, it’s likely that as a proportion, Ireland will be asked to accommodate between 1,800 or 2,000.
“I think we would have no difficulty accepting those numbers and may go beyond it,” Mr Coveney said.
“The Government wants to be generous but also we want to make sure that whatever decision we make to relocate refugees results in us being able to do that in a way that is compassionate and proper as regards housing needs and healthcare needs and supports.
“What we shouldn’t do is make offers that we can’t deliver on later on and results in seeing refugees homeless in Ireland — that isn’t something that I think we can allow happen.
“We want to be generous, open-minded and open-hearted in relation to what is an awful human tragedy that is unfolding and huge numbers of people are involved in that — we need to be as generous as we can be within reason and make sure that we follow through on that fully.”
Mr Coveney was speaking yesterday after aid campaigner Bob Geldof branded the EU response to the crisis to date a “fucking disgrace” and pledged to open his homes to refugees.
“It is a monstrous betrayal of who we are and what we wish to be,” Geldof said.
“We are in a moment that will be discussed and impacted upon in 300 years’ time, a fundamental shift in the way the world has worked for the last, say, 600 years.
“If there’s a new economy there needs to be a new politics. There isn’t and it’s that failure of new politics that has led to this fucking disgrace ... this absolute sickening disgrace.”
Speaking to Dave Fanning on RTÉ radio, Geldof said that he would open the doors to his family home in Kent and his flat in London to refugee families.
“I’m prepared — I’m lucky, I’ve a place in Kent and a flat in London — me and [partner] Jeanne would be prepared to take three families immediately in our place in Kent and a family in our flat in London, immediately, and put them up until such time as they can get going and get a purchase on their future.”
Meanwhile, Irish advocacy group Uplift has received over 6,000 responses to its Pledge a Bed campaign for people to share their homes with refugees.
And donations are expected to flood in today to a major aid convoy leaving Cork for Calais at the end of the month.
The Cork Calais Refugee Solidarity Group will collect clothing, bedding, sanitary and medical supplies, and any cash donations, at its warehouse in Marina Commercial Park throughout the day.
A collection, which will feed in to this aid convoy, will also take place in the Church of Ireland grounds in Blarney from 9am to 11am.