Faith groups should be made to register with the authorities if they want to provide education and youth provision, safeguarding leaders have told an inquiry.
The Independent Inquiry into Child Sexual Abuse (IICSA) also heard concerns child abuse within religious groups and institutions was still being under-reported across England.
The inquiry was hearing evidence as part of the child protection in religious organisations and settings investigation.
Leaders from three council areas' children's safeguarding teams said they believed there was still under-reporting.
All agreed there should be the creation of a formal registration system, providing a database of contacts for every religious institution.
They were also giving evidence about challenges in communicating safeguarding responsibilities to the large and diverse numbers of faith groups in the local authority areas of Birmingham, Leeds, and the London borough of Tower Hamlets.
The inquiry heard that in Birmingham, with a population of 1.4 million, there had been 3,000 child safeguarding referrals to the authorities between 2017 to 2019, with 3.6% of those related to a faith setting.
The "vast majority" of those related to the Church of England (CoE), the Roman Catholic church, Pentecostal and free churches and "with a third pertaining to mosques", barrister to the inquiry Fiona Scolding QC said.
In Leeds, between 2013 and late 2019, there were 105 referrals, with about half in relation to "mosques and madrassas".
Jasvinder Sanghera, independent chair of Leeds Safeguarding Children's Partnership, told the inquiry the vast majority of reports had come from "via schools, mainstream institutions - rather than from the institutions themselves".
In Tower Hamlets, between November 2018 and October 2019, there were just "three referrals against pastoral staff, in a religious setting" and only one which concerned allegations of a sexual nature.
Richard Baldwin, Tower Hamlets' director for children's social care, said: "I think that figure is an under-reporting."
Ms Sanghera echoed that view, adding she did not believe the numbers of referrals in Leeds were representative.
Graham Tilby, assistant director for safeguarding in Birmingham Children's Trust, said: "It's a similar picture to what has been described in Leeds, it's a low-level of reporting directly from religious settings as opposed to police and schools."
He added: "Fundamentally, I think it reflects an under-reporting across all faiths, but particular faiths as well."
Those giving evidence to the hearing were asked what more could be done to increase referrals.
Mr Baldwin said there needed to be a continuing of voluntarily "engagement" with faith groups, which the inquiry panel had heard was already ongoing.
He also called for, in his statement to the inquiry, all out-of-school settings and provision - faith-based or not - to be compelled to formally register with the Department for Education (DfE) and the local authority.
Mr Baldwin said the reason for his calling for a "broad" registration, beyond just religious settings, was "there is a worry the debate becomes far more focused on the state interfering with religion".
He added that it was "a debate to be had" as to which organisations held and managed such a register, but there was "a role for local authorities".
Ms Sanghera said registration should "absolutely" be introduced.
She said: "If we really mean what we say, that safeguarding is everybody's business, it cannot be the case that preserving one's cultural beliefs and values trumps safeguarding.
"This is about our concerns about children and the risk to children and actually it's important all faith organisations respond to the requirements expected by the law and society.
"Why wouldn't they engage in that, they've got nothing to hide."
She added: "We should have registration, possibly with the DfE and the local authority."
"A compulsory register, will enable us to keep track of the children we are concerned about", she said, adding it was "about openness and transparency".
The inquiry was told by Ms Scolding there had been "very significant opposition", including from some faith groups, to a 2015 suggestion by the DfE for such a registration scheme.
Ms Sanghera said: "I don't understand how anybody can make an argument against safeguarding and if they are, let's challenge it."
Mr Tilby said: "There is something about a register where you are required to register and make sure the local authority - and I think that is the best place to do this - has an over-arching database of places of worship, key contacts within that organisation.
"So where there are safeguarding issues, you don't waste a lot of time trying to find out who to talk to."
He added that there should be "a national body that sets national standards of safeguarding across all the sector", but that existing "reputable" non-governmental groups should continue working with faith-based groups.
"If you have something distant that is being imposed by the state, there is a risk of organisations going underground," he added.
The latest phase of the IICSA is looking at how child protection is handled in religious organisations and settings in England and Wales.
These include British Judaism, Islam, Jehovah's Witnesses, Baptists, Methodists, Sikhism, Hinduism, Buddhism and non-conformist Christian denominations.
The inquiry has already held separate investigations into the Roman Catholic Church and the Anglican Church.