The Education Minister Richard Bruton insists there are adequate numbers of teachers being trained to meet demand.
However, Mr Bruton admits initiatives are being taken to ensure all subjects are adequately covered.
He was responding to figures showing a drop of 62% in the numbers applying for teacher training courses in the last five years.
There were just 1,068 applications for second-level training courses last year, compared to 2,824 in 2011.
The Catholic Primary Schools Management Association (CPSMA) says 90% of its 2,800 schools are having problems finding teachers.
It is also reported that there are major shortages of teachers for key subjects like Irish and maths.
Minister Bruton has admitted there is a problem getting substitute teachers to fill short-term positions, and said an upturn in the economy can be linked the shortfall.
Minister Bruton says there are steady numbers graduating.
He said: "There is a lot of competition out there with a recovering economy and obviously there are a lot of different routes that people can go.
"But we are seeing steady numbers of graduates coming out all the time - as I say 3,000 graduates coming out each year.
"That should be enough to meet our needs, but we have been recruiting rapidly in recent times."
Speaking on Newstalk's The Hard Shoulder, he said initiatives are being taken to ensure all subjects are adequately covered, adding that his department is looking at a number of options to tackle the shortfall.
Mr Bruton said: "We are looking at enhancing the period that people on career breaks can work – they are now confined to 90 days
"We are pointing out to schools and encouraging schools to recognise that people who are in their final year of teacher training can take up these posts and a lot of it is very good for their own development."
- Digital Desk