Minister for Education Ruairi Quinn has invited patronage bodies to apply to run four new primary schools due to open in September of next year.
The new schools will be in counties Cork, Dublin and Galway.
In a statement, Mr Quinn said parental demand would be the key issue in deciding which groups would be awarded patronage.
Existing diversity of patronage in each of the four areas would also be taken into account.
The schools are among 20 new schools announced recently to meet rising enrolment.
Seven new schools opened last September and five are due to open this year.
The Department of Education is forecasting an increase of over 45,000 in the number of children attending primary schools by September 2017.
Protest at delay over opening of Kildare national school
Meanwhile, primary school pupils and their parents demonstrated today in protest at the delayed opening of their new school building in Co Kildare.
Parents of children in St Anne's National School said it was more than 16 months since work had halted on the almost complete building, but it was still shut.
The 250 pupils in the Ardclough school are currently housed in mice-infested prefabs.
The new school building was completed in December of 2011, but a health and safety check carried out in January found defects.
Last September, the Department of Education terminated the contract with the company, called Glenman.
The project has since been retendered.
The Department said the health and safety of pupils and their teachers is of the utmost concern and it hoped work to complete the project would resume next month.
The school said it hopes this means the school will be open on time for next September.
The Department would not comment on why the contract with Glenman was terminated. RTÉ News contacted the company but has received no response.