Plans to force new faith schools in England to select more pupils from other religions are to be scrapped.
A voluntary agreement has been reached instead, Education Secretary Alan Johnson says.
The Catholic Church had joined the Church of England in agreeing that up to 25% of places should go to pupils from another faith or none, he said.
The plans were introduced in an amendment to the Education and Inspections Bill last week.
The amendment would have enabled councils to require new faith schools to select up to 25% of their intake from pupils of other faith backgrounds or those with no religious beliefs.
"We've made enough progress through the voluntary route that we don't need the blunt instrument of legislation"
Its abandonment followed talks with representatives of all the UK's major religious groups.
There had been a "consensus amongst all faith groups" that "every school whether faith or non-faith should have a duty to promote community cohesion", said Mr Johnson.
"We've made enough progress through the voluntary route that we don't need the blunt instrument of legislation," he added.
Ofsted would inspect all schools on the community cohesion element, Mr Johnson said.
"You should encourage schools to engage on the basis of social responsibility by opening up places... not by passing draconian laws"
"What we have found in dialogue with the Muslim schools, for instance, is they have a policy where they want between 20% and 25% of pupils to be from outside of the Muslim faith," he added.
"They make the point that very few people want to take them up and they say that's about misconceptions about Muslim schools."
Mr Johnson's plans last week provoked protest from Catholics and other faith groups.
The Catholic Archbishop of Birmingham, Vincent Nichols, described Mr Johnson's proposed amendment as "ill-thought-out, unworkable, contradictory of empirical evidence and deeply insulting".
The Archbishop, who chairs the Catholic Education Service, on Thursday evening said he welcomed the "broad agreement" which had now been reached.
'Dog's dinner'
Shadow Schools Minister Nick Gibb welcomed the development, saying the Conservatives had always believed the faith school issue had been one "for schools themselves to decide".
ENGLAND'S FAITH SCHOOLS
"You should encourage schools to engage on the basis of social responsibility by opening up places, by involving themselves in the community, but not by passing draconian laws forcing schools to adopt a quota of pupils from non-faiths or from other faiths," he told BBC News.
The government said the move was an example of a "listening government".
But Liberal Democrat education spokeswoman Sarah Teather said the whole affair had been a "dog's dinner".
"The government first of all announce there were going to be quotas and then they found out that in fact there was a huge backlash to that and they had to row back from it.
"They don't seem to have been clear about what the problem is," she said, adding: "If we're going to deal with this kind of problem you need to build consensus, you need to take a long term view."
The National Secular Society said the latest development would not make any difference.
"How many people are going to send their children to a minority faith school where quite possibly there's going to be a compulsory jilbab and hijab uniform? They're just not going to do it," executive director Keith Porteous-Wood said.
"The real issue is how we're going to get some kind of cohesion...
"I think the people who ought to be having a duty to promote community cohesion is the government itself and it's failing miserably."
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