The seasonally-adjusted rate of unemployment has fallen by 3,000 to 201,600, the lowest level since October 1983, according to figures from the Central Statistics Office.
The unadjusted figure for March fell by 6,377 to 201,234, with 70 per cent of the drop accounted for by males.
In the last year, the seasonally adjusted rate has fallen by 33,500, the CSO said. Seasonally-adjusted unemployment for under-25s fell from 39,400 to 38,800.
The Republic now has an unemployment rate of 6.7 per cent, down from 6.8 per cent for the month before, which compares with an EU average of 9.8 per cent.
According to the most recent figures, the EU states with lower rates than the Republic are Luxembourg (2 per cent), Netherlands (3.6 per cent), Austria (4.4 per cent), Portugal (4.4 per cent) and Denmark (4.6 per cent).
Germany (9.5 per cent), France (11.7 per cent) and Spain (18.2 per cent) have had higher rates than the Republic for more than a year.
The Government chief whip, Mr Seamus Brennan, said the latest figures were "continuing evidence of the ability of the Irish economy to translate current strong growth into jobs".
He said it was the 24th consecutive month in which there had been a fall in the seasonally-adjusted live register figure. The Government's Fastrack to IT (FIT) programme, which aims to train unemployed people for jobs in the IT sector, would take another 3,500 people off the live register, he added.
The Irish National Organisation for the Unemployed (INOU) welcomed the figures, but said there was still a long way to go. Other problems associated with unemployment were now becoming evident, INOU said.
"As unemployment continues to fall, the people who are left are increasingly isolated," said chairman Mr Barrie McLatchie.
The Labour Party spokesman on Enterprise, Trade and Employment, Mr Pat Rabbitte, said the State still had an "unemployment crisis" and the Government was finding it difficult to get work "for people who have been without employment for over 5 years".
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