The number of people signing on the live register fell by 1,300 in January to 137,800, the lowest seasonally adjusted figure since December 1981, according to the Central Statistics Office.
In the year to January 2001, the live register decreased by 34,091 persons, the office stated.
Welcoming the figures, the Tanaiste, Ms Harney, said there were now almost 113,000 fewer people on the live register than in June 1997.
"Nonetheless, our success in achieving an unemployment rate of 3.6 per cent, one of the lowest in Europe, should not make us complacent," Ms Harney said. "It is still one of my key aims to reduce this further and, in particular, to reduce long-term unemployment. I believe that the policies and strategies being adopted by this Government will ensure that we continue to be the most attractive location in Europe for foreign direct investment notwithstanding fears expressed in some quarters in this regard."
But the Labour Party spokesman on enterprise, trade and employment, Mr Pat Rabbitte expressed concern over the surge in job losses announced during December and January.
"The live register figures for the past two months have begun to show some negative trends. These trends will be further compounded when the job losses, announced throughout December and January, take effect," he said.
The unadjusted figure rose marginally by 485 in January to 142,071, according to the CSO.
The Border, Midland and Western region experienced the largest increase in the number on the live register at 673. Against the overall monthly increase, the live register fell in Dublin and the south-west.
Those on the register under 25 years increased by 1,125, while the number aged 25 or over decreased by 640.
"We have warned that young people leaving school without qualifications would be the first to suffer in the event of a downturn in the jobs market," said Mr Rabbitte.
The Irish National Organisation of the Unemployed (INOU), citing an Irish Times/MRBI opinion poll, said jobs and unemployment remained a key concern for one in five Irish voters and ranked higher as a concern than taxation or education.
"Despite the continued decline in live register numbers, approximately 4,500 people join the live register every week," said Ms Camille Loftus, welfare-to-work co-ordinator of the INOU.
"The experience of mass unemployment remains fresh in people's minds, and the recent spate of job losses reminds them of the poverty and despair of unemployment."