The number of trips to Ireland by overseas visitors increased by 2.1% in September, compared to the same month last year.
British visitors numbers went up by 6% while other European visitor numbers rose by 3.6%.
There was a slight increase of just over 1% in the numbers travelling from long haul routes.
However, there was a 4% drop in the numbers travelling from North America to Ireland in September.
"The CSO figures continue to indicate a very mixed picture – with a small increase in arrivals from Britain (+0.6%), a modest performance from Mainland Europe (+2%), arrivals from North America up +3.7% and from long-haul markets up +6%," said Niall Gibbons, CEO of Tourism Ireland.
"However, North America is showing a weaker pattern as the year unfolds – down -4% for the month of August.
The continued uncertainty around Brexit poses a real and ongoing concern for Irish tourism.
According to recent research conducted by Tourism Ireland in Britain, France and Germany, there is a heightened risk of consumers postponing trips due to uncertainty.
"The fall in the value of sterling has made holidays here more expensive for British visitors – and has made Britain more affordable for visitors from many of our top source markets," said Mr Gibbons.
"We very much welcome the additional €6 million which was allocated to Tourism Ireland in the recent budget – to be used for promotional campaigns between now and the end of 2019.
"The additional funding allows us to roll out strong end-of-year campaigns, which will deliver a message of reassurance to prospective visitors around the world.
"This funding will also complement our existing programme of activity for Q4, allowing us to undertake kick-start campaigns in our key markets, to position us well for 2020."