Amanda Spielman, the chief inspector, criticised the Church of England for opposing the idea and insisted new legislation was necessary to monitor "what is happening under the radar in so-called out-of-school provision".
Speaking at the Church of England's Foundation for Educational Leadership annual conference, she called on ministers to update legislation and give Ofsted more powers to regulate settings where children are educated outside of school hours.
The new head warned that intervention in places such as Sunday schools and Bible clubs was needed due to ensure "the small minority of settings that promote extremism are not able to evade scrutiny".
The proposals were first made under former Prime Minister David Cameron's government but a personal intervention by the Archbishop of Canterbury and a group of crossparty MPs, who labelled the proposals "bewildering" in 2016, halted the plans.
However, the head of Ofsted insisted regulating Sunday school classes won't lead to "a troop of inspectors turning up at Sunday schools".
The Department for Education wanted to force institutions teaching under-19s for more than six hours a week to register with the government.
Spielman added: "If we are to protect many of the tenets that the Church holds dear, we need the power to tackle those trying to use education to undermine them."
She also called on head teachers to "tackle those who actively undermine fundamental British values".
"Rather than adopting a passive liberalism, that says 'anything goes' for fear of causing offence, schools leaders should be promoting a muscular liberalism," she said.
The Christian Institute was specifically referenced by Spielman as a group with "conservative" views.
Responding to her comments, Simon Calvert from the charity told Premier: "Muscular liberalism shouldn't mean some kind of aggressive secularism - and that's the danger."
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