Official figures show that the number of people signing on climbed in May, having fallen back slightly in April.
The Central Statistics Office said the seasonally adjusted Live Register figure rose by 6,600 from April to reach 439,100 - a record high.
This brought the jobless rate up to 13.7% from 13.4% in April.
The Live Register figures had shown little change in the early months of the year, leading to suggestions that the rise in unemployment could be stabilising.
The headline figure, which does not take seasonal factors into account, was up by 5,265 to 437,922.
The number of people on the dole in May was just over 11% higher than a year earlier.
The May rise in the Live Register was the biggest monthly increase since August last year and surprised most economists.
A spokesman for Minister for Enterprise, Trade & Innovation, Batt O'Keeffe has described the latest increase in the number of workers signing on as 'relatively modest'.
He said that while the figures showed a seasonally-adjusted monthly increase of 1.5%, they followed two months of solid stabilisation in the Live Register.
The spokesman added that the continuing downward trend in redundancies showed that the labour market was beginning to reflect greater economic stability and signs of recovery.
He underlined that last month's figure for the number of redundancies notified to Mr O'Keeffe's Department was lower than that for any single month last year and the lowest since December 2008.
ICTU says unemployment higher than 13.7%
However, the Irish Congress of Trade Unions has said that the 'true' unemployment figure is far higher than the official count of 13.7% reported by the CSO.
It says that it could be as high as 18.5% when other groups of people are added.
It says these include the unemployed who have been forced to emigrate, those who have stayed in or returned to education because they cannot find work and people who can only get part-time or casual jobs.
ICTU Economic Advisor Paul Sweeney said that about 100,000 unemployed people are not included in the CSO figure.
He says the principal factor hiding the true level of unemployment is emigration.
The ESRI estimates that a net 60,000 people will leave Ireland this year and 40,000 next year.
Central Bank Governor Professor Patrick Honohan said last week that unemployment in Ireland had stopped growing, but that it was probably due to migration flows and the withdrawal of people from the labour market.
Fine Gael's Labour Affairs & Small Business Spokesman Damien English said: 'There are more people out of work this week than at any time in Irish history.
'Yet Enterprise Minister Batt O'Keeffe is more interested in spending his time attacking Fine Gael than sorting out the unemployment crisis.
'Minister O'Keeffe and his team would be better off explaining why his Government has still not formulated a job creation strategy.'
