The Catholic Education Service is opposing a plan for new faith schools in England to have to give a quarter of places to non-believers.
Director Oona Stannard said faith schools were "not part of the problem".
An amendment to the education bill is being tabled by Lord Baker, who called "exclusive" faith schools "divisive".
Education Secretary Alan Johnson said he thought the amendment "good sense". But Muslim and Jewish representatives have also criticised the idea.
Northern Ireland 'example'
In a lengthy statement issued by the Catholic Education Service for England and Wales, Ms Stannard said the governing bodies of Catholic voluntary aided (VA) schools were the admissions authorities "and should remain so without political interference".
"Their role should not be compromised by a requirement to implement social engineering through externally imposed admissions quotas," she said.
"Schools with a religious character are part of the solution for society, not part of the problem."
But Lord Baker said children were being divided at the ages of five and 11.
"And we've only got the example in Northern Ireland to see where that leads," he said.
The exclusive Muslim schools were very exclusive, he said.
"The selection criteria is that they make it clear that they want to create a total Muslim personality, and at the age of 11 pupils are asked if they've read the Koran, or are they fluent in Arabic, have they learnt the prayers.
"That means that children of other faiths will not apply. And I think that further divides society."
Mr Johnson said he saw good sense in Lord Baker's move: "There is an issue about community cohesion."
He referred to the Church of England's recent move, adding: "I think that is very good and the feeling in Parliament is that should be repeated by other faiths."
The Conservative Party also welcomed the proposals.
Shadow education secretary David Willetts said Catholic schools had achieved a better social and ethnic mix than other local schools.
"It may be the case that when it comes to Muslim schools, part of the problem is that the Muslim faith group is also associated with a set of social and ethnic divides," he said.
But Tahir Alam, who chairs the education committee of the Muslim Council of Britain, said the proposals would not help integration.
"I think this particular amendment that's going through has not been consulted on at all - although the arguments relating to integration are laudable.
"But I don't think this is the only way - or the best way - of achieving that.
"Locking two people in the same room... is not the best way of creating integration."
The chief executive of the Board of Deputies of British Jews, John Benjamin, was sceptical, although he said non-Jewish children were welcome at Jewish schools.
"It does happen in places where the demographics don't support a completely Jewish school - and that is a matter of parental choice.
"But I think it would be nonsensical, where the demand exceeds the supply of places at Jewish schools, for Jewish children to not have the opportunity to go to Jewish schools because of a quota system," he said.