Overseas visitors made 596,000 trips to Ireland in September, down 2.6% on the same month last year, according to the Central Statistics Office.
For the first nine months of 2004, the number of visits was up 2.8% at just over 5.1 million.
A breakdown showed that the number of visits from Britain in September was down by more than 6% on the same month last year at 322,000, while visits from other European countries were 7% lower at 135,300.
Visits by North American residents rose by 10.7%, however, to just over 104,000.
Irish residents made 538,400 trips abroad in September, up 11.4% on the same month last year.