Around 20,000 people have applied for the 300 positions with An Garda Síochána since the force re-opened the application process for new recruits last month.
It is the first time people have been able to apply since a recruitment moratorium was introduced in 2009.
Minister for Justice, Equality and Defence Alan Shatter said he was “greatly encouraged by the positive response”.
“This is the first recruitment campaign to An Garda Síochána since 2009 and it is recognised by all as being a welcome and important development,” he said.
The closing date for applications, which can be submitted online through publicjobs.ie, is midnight on Thursday.
The first round of new recruits will enter the Garda College in Templemore, Co Tipperary later this year to begin the 32 weeks of training required before they are posted to stations.
There are now fewer than 13,100 gardaí, almost 1,600 less than the peak levels of 14,600 just after the economy collapsed.
