The Government has launched a consultation over its First Homes scheme, which proposes to cut the cost of some new homes by a third for first-time buyers.
It aims to give people the opportunity to buy a home in their local area, saving eligible first-time buyers around £100,000.
The discount will be prioritised for veterans and key workers such as nurses, police officers and firefighters.
The scheme will see the discount applied in perpetuity, so when the home is sold in future, the new local buyer will also be able to buy at a discount.
However, the LGA says councils need discretion on the number of First Homes required in new developments to ensure a mix of homes are available, as not everyone is ready to buy.
Cllr David Renard, LGA Housing Spokesman, said: “Councils support measures to enable home ownership. It is important that this does not come at the expense of providing truly affordable homes for rent.
“Not everybody is ready to buy and we will be making the case in this consultation that local areas will need discretion on the number of First Homes required in new developments. This will allow councils to ensure a mix of homes – to rent and buy – are available and affordable to people that need them.
He added: “A genuine renaissance in council house building would increase housing supply, boost home ownership and reduce homelessness.
“For that to happen, the Government needs to use the forthcoming Budget to reform Right to Buy, by allowing councils to keep the receipts of homes sold under RTB in full and to have the flexibility to set discounts locally.”