The unemployment rate remained unchanged between June and July at 7.8%, with 169,100 people registered as unemployed last month.
According to the figures from the Central Statistics Office, July was the second consecutive month where there was no drop in the level of unemployment.
The last time the unemployment rate remained unchanged for three months was between August and October of last year, when the rate was 9.1%.
The annual drop in unemployment for July was 1.4% or 29,800.
Meanwhile, there was a slight increase in the youth unemployment rate in July, which rose by 0.6% to 16%.
There are now just over 30,000 15-24 year olds out of work across the country.
Chief Economist with Davy Conall Mac Coille said the CSO figures do not necessarily indicate a drop-off in the reduction in the rate, due to possible revisions.
He said: "At face value, this could be taken as evidence of a slowdown in the Irish labour market - but the initial estimates tend to be revised heavily.
"Also, it is too early to discern any negative effect from Brexit on Irish companies' hiring decisions. We still do not expect any significant impact on the pace of Irish employment growth from Brexit until late 2016 at the earliest."
According to the figures from the Central Statistics Office, the unemployment rate for men last month stood at 9.1% (107,900), while the rate for women was 6.2% (61,200).
The Irish Small and Medium Enterprises Association has attributed the static rate of unemployment to high business costs.
ISME CEO Mark Fielding said: "The cornerstone of productivity and competitiveness is cost control and it is time that the Government became more involved in tackling cost-creep across the business sector".
