Education Minister John O'Dowd has said he would like to see the certificate in religious education that is required to teach in Catholic primary schools scrapped.
Mr O'Dowd said any decision about the issue lies with the first and deputy first ministers.
He said he had written to them several times about it, but had not received an answer.
The certificate is not required for teaching in secondary schools.
St Mary's teacher training college in Belfast says the certificate assists teachers to educate children according to Catholic principles.
However, the DUP's Nelson McCausland said its requirement was viewed as discriminatory.
During question time in the assembly, Mr O'Dowd also said he did not want to see any reduction in the numbers of people being trained at St Mary's and Stranmillis teaching colleges, as the loss of the centres would have implications for the economy.
In reply to a question from Trevor Lunn of Alliance, the minister said the current annual intake was 165 for St Mary's University College and 169 for Stranmillis University College, and that numbers had been cut by 30% in recent years.
Mr Lunn said that only 18% of new teachers found jobs within a year of graduation, and asked how the minister could justify training places "for probably more than 50% more than the number of teachers we actually need".
Mr O'Dowd said he believed it would be a mistake "to lose that economic driver which is in our communities", and that "what we can do instead is we can close our teacher training colleges down and send all those young people over to England".
Also during question time, Employment and Learning Minister Stephen Farry said he found the attitudes expressed by some of those protesting against the removal of funding from St Mary's to be "absolutely shocking".
The minister had previously announced his intention to remove the small and specialist institution premium funding from both St Mary's and Stranmillis.
Sinn Féin's Cathal Ó hOisín accused the minister of conducting a "continuing crusade against St Mary's".
The minister said an unsustainable, artificial teacher training system was being subsidised, and there was a need for reform.
Mr Farry said he had been "quite shocked" by a meeting he had with St Mary's students.
"People were saying that they didn't feel safe celebrating their Irish culture outside the context of St Mary's," the minister said.
He considered this "an incredibly strange and narrow approach to be taking".
"They were quite happy having gone to a Catholic primary school, Catholic secondary school, to go to a Catholic-based third-level education system, because they are going to go on to a Catholic secondary school, or a Catholic primary school, so why do they need to mix with anyone else in society?" Mr Farry said.