New figures, released by the Irish Tourist Industry Confederation, also show that those holidaying at home are taking shorter, cheaper trips.
Close to 6.5 million people travelled to Ireland from overseas in 2012, which is around the same figure as 2011.
The Irish Tourist Industry Confederation says it was a year of "mixed fortunes", with a 2% growth from mainland Europe and North America off-set by 100,000 fewer visitors from Britain, Ireland's largest source market.
Dublin, it says, had a good year but other parts of the country saw fewer tourists.
A fall-off in demand during peak summer months, with arrivals down 7% in July compared to 2011, was described by the Confederation as disappointing.
It says that given the economic situation and the unfavourable Irish weather, the domestic market performed reasonably well, but that those holidaying at home were taking less frequent and shorter trips.
The outlook for 2013 is said to be moving in a positive direction.
The Confederation says the year-long Gathering initiative has the potential to deliver a 5% growth in arrivals.