Madrassas in England will face regulation and inspection under government plans published on Thursday.
Last month, Prime Minister David Cameron said some children were "having their heads filled with poison and their hearts filled with hate" in these Muslim supplementary schools.
Muslim organisations accept regulation is needed to protect children's welfare but maintain concerns about radicalisation are misplaced.
The UK contains about 2,000 madrassas.
Under the plans, any out-of-school setting providing intensive education would be required to register and be open to inspection.
This is likely to cover almost all madrassas, as the proposals suggest six to eight hours a week as the threshold for regulation.
Many Muslim children attend madrassas to learn Arabic in order to recite the Koran and understand the principles and practices of their faith.
The plans suggest there would be a range of prohibited activities that could prompt intervention: from appointing unsuitable staff to failure to ensure the safety of children.
Corporal punishment would be banned, along with teaching that "promotes extreme views" or is deemed incompatible with fundamental British values.
New powers would be created to impose sanctions, which could include closing down premises or banning individuals from working with children.
Inspection would be "risk-based" rather than routine, following concerns raised by parents or children or random visits.
Many madrassas did a good job, a Department for Education spokesman said.
"We recognise that many out-of-school education settings, including supplementary schools and tuition centres, do a great job in supporting children's education and development - but, without proper oversight, there is a risk that some children attending them may be exposed to harm, including from extremism."
Many madrassas are large voluntary organisations that vet and train their staff, but others operate in smaller informal settings.
And while Ofsted has intervened in a number of informal education settings, it has made clear its powers to do so are limited.
'Safe and secure'
Zulfi Karim, of the Bradford Council of Mosques, said madrassas needed "to do more to prevent abuse, and we could be more inclusive".
"That's no different to society overall, these issues are not exclusive to the Muslim community alone," he said.
Mr Karim also voiced concern the government risked interfering with religious instruction.
"We would like our Islamic institutions to remain independent, and we will play our role in making sure that they are safe and secure for the community they serve," he said.
Between 450 and 500 children attend the Quwwatul Islam madrassa in Preston, Lancashire, every afternoon after school.
The local Muslim community raised money for the building, which also houses a nursery rated outstanding by Ofsted.
Khalid Ibrahim, the madrassa's head teacher, is confident it would comply with all the welfare standards but said it was not clear what problem the new regulations were intended to fix.
"That's exactly what we don't understand, simply because there is so much positive work taking place, based on the announcement it looks like we are the problem to the wider problems in society, rather than the solution," he said.
Pascale Vassari from the National Resource Centre for Supplementary Education said there should be the same standard for everyone,
"Every child has a right and every parent has a right to know the activities they attend are safe," he said.
Earlier plans for a voluntary code for madrassas were shelved by the Department for Education last year.
A consultation on the plans will run until 11 January.
The government says the consultation will gather more information on the number, size and variety of out-of-school settings that might be covered by the new regulations.