Sinn Fein reject Robinson's comments on education
Sinn Fein has accused the first minister of launching an attack on the Catholic education sector.
In a speech on Friday, Peter Robinson described the Northern Ireland education system as a "benign form of apartheid".
He said the current system, where Catholics and Protestants are usually educated separately, must change.
SF MLA, John O'Dowd said his focus should be on the bureaucracy within the system and not Catholic education.
"The principle of children going to school together, no-one can argue against," he said.
"However, I suspect that is not the motivation behind the DUP leader's statement last night.
"What we are witnessing is an attack on the Catholic education sector, not based on the principle that the DUP support integrated education.
"It's rather based on the principle that the DUP are opposed to the education sector which the Catholic Church has promoted, quite successfully it has to be said.
"Those within the DUP can't live up to reality that what is needed is a complete modernisation of the bureaucracy that surrounds it."
Mr Robinson also said he wanted to set up a commission to look at the total integration of the different sectors.
He compared the system to South Africa during apartheid where black and white children were educated separately.
BBC NI education correspondent Maggie Taggart said the speech was likely to provoke controversy.
In an apparent reference to Catholic schools, he said he had no objection to church schools but he did object to the state paying for them.
"It may take ten years or longer to address this problem, which dates back many decades, but the real crime would be to accept the status quo for the sake of a quiet life," he said.
"The benefits of such a system are not merely financial but could play a transformative role in changing society in Northern Ireland."
He added that there were a number of "knotty issues" such as "religious education, school assembly devotions and the curriculum".
"Future generations will not thank us if we fail to address this issue," the DUP leader said.
It would be difficult to dislodge "vested interests", he said, but was "convinced" that it should be done.
Our correspondent said that the DUP position has been that the state - or controlled - sector was non-denominational and could be used by those of all religions and none.
She added that Mr Robinson was proposing a single education system, rather than enlarging the integrated system which he did not believe would create the critical mass needed to make a real difference.
However, Noreen Campbell from the NI Council for Integrated Education has said Mr Robinson's speech is a significant contribution to the debate.
"For the first time, a major politician has said that a separate system of education is not good for our society generally - that there are moral issues about it," she said.
"He has actually made some of the points we in the integrated movement have been making for years and he has said that there ought to be a major commission to look at educational provision here in Northern Ireland, that has got to be welcomed."