The unemployment rate fell to 4.4% in May, according to figures from the Central Statistics Office.
It was down from a rate of 4.6% in April.
It compares favourably to a figure of 5.9% unemployment in May of last year.
That means the economy has exceeded the threshold for what's commonly referred to as full employment, a rate of 5% unemployment.
The seasonally adjusted number of unemployed people stood at 108,200 in May.
That was down from 111,300 in April.
The seasonally adjusted unemployment rate in May was 4.7% for males and 4.2% for females.
Youth unemployment - which covers those aged 15 to 24 - stood at 10% in May.
That was down from 10.3% in April.
Commenting on the figures, Pawel Adrjan, economist at global job site Indeed, said at 4.4%, the rate of unemployment is now at its lowest level since since 2005 and close to historical lows.
"Whilst there will likely be commentary around the economy being close to ‘full employment’ there is ample evidence to suggest that Ireland’s job boom has not yet run out of steam," he said.
"The most recent data shows employment growth is still robust with a seasonally-adjusted quarterly growth rate of 1.5% in Q1 2019, compared to Q4 2018. There are also still almost 20,000 job vacancies, with the vacancy rate showing no signs of falling.
Andrew Webb, Chief Economist at Grant Thornton Ireland, said the focus would now turn to whether or when the unemployment figures will fall to below 100,000.
"This looks set to be by early autumn on current pace."
He said the improvement would raise questions around skills and talent retention.
"In an increasingly tight labour market, the challenge for employers is to find new staff and keep the staff they have. It feels increasingly like a sellers market, as evidenced by increasing wage rates."
Economist Alan McQuaid said the figures indicated that the rise in employment was far from over.
"The latest Labour Force Survey figures showed that the participation rate stood at 62% in the first quarter of 2019, compared with a pre-recession peak of 66.7%. Greater participation should slow down the fall in the jobless rate.
"The average jobless rate is projected to fall to 4.5% this year from 5.7% in 2018 even with this unemployed economist adding to the numbers out of work."