Tourism Ireland says the number of tourists traveling from Britain to Ireland remains a concern.
This is despite the figure actually increasing for January to July this year.
According to the Central Statistics Office (CSO), arrivals from Britain are up 2.5%.
However Tourism Ireland says it is too early to say if this represents a turnaround in the long-term trend.
"The impact of Brexit on outbound travel from Britain, therefore, remains a concern", it adds.
Overseas visitor numbers increased by almost 8% during the January-July period, 436,000 additional overseas arrivals when compared with the first seven months of 2017.
North American growth
This was the best ever month of July for Irish tourism, with more than 1.16 million arrivals.
Niall Gibbons, CEO of Tourism Ireland, says North American figures are "particularly welcome", which saw growth of 13.5%.
"A number of factors are working in our favour, including more airline seats than ever before, from more gateways across the US and Canada.
"We've also seen excellent results from mainland Europe, up 10.6% on January-July last year, with particularly strong performances from Germany (+20%) and Italy (+15.5%).
"Tourism Ireland has prioritised North America and mainland Europe, as markets which offer a strong return on investment, in terms of holiday visitors and expenditure."
He says their aim is to grow overseas tourism revenue in 2018 to €6bn.