Ministers had wanted to gain greater control of "out-of-school education settings" in a bid to tackle extremism.
It would have seen groups that teach children for more than 6-8 hours a week having to register.
The plans were widely criticised by Christian groups who feared they amounted to state regulation of church.
The government put the plans to consultation but around three quarters who took part disagreed with them.
Announcing the U-turn, the Department for Education said: "We want to ensure any future system of regulation that we may introduce appropriately targets the small minority of settings which may be exposing children to harmful practices, without causing undue burdens on the sector as a whole.
"We believe it is equally important that we ensure any future system carefully takes into account the differences within such a diverse sector, where settings vary considerably in terms of their characteristics and types of activity and education they offer."
Welcoming the government's response, the Evangelical Alliance (EA), which lobbied against the plans said it was a victory for religious freedom.
Dr David Landrum, director of advocacy at the EA, said: "As we expected, the report shows how strongly faith groups, parents and others feel about proposals to register and regulate out-of-school settings, and in particular about the role of Ofsted.
"Indeed to many these proposals, which were launched by former education secretary Nicky Morgan, represented a classic example of religious illiteracy.
"These proposals would have had a profound effect on religious freedom and fundamental human rights, and consequently we welcome the news that the Government are listening to the concerns of those who responded."
The EA says it will "retain a watchful eye" on other proposals which may replicate the government's original plans.
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