The right of religious-run schools to give priority entry to children who are baptised should be restricted to those living in their catchment area, according to the Labour Party.
Current practices see some Catholic schools enrolling baptised children from other parishes, rather than an unbaptised child living closer to the school.
Labour is seeking Dáil support for a bill to amend the section of the Equal Status Act that gives the religious the right to use admission policies to protect their ethos.
Labour said it accepted there would be constitutional difficulties in attempting to eliminate the so-called "baptism rule". The party's education spokesperson Joan Burton said they were taking this approach because they believed it was achievable, and would make a difference.