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The Federation, which represents England's housing associations, said the target, if met, would help to drastically reduce fuel poverty by making homes more energy efficient, and also tackle climate change.
NHF Chief Executive David Orr said: "We welcome the Government's ambition of dramatically cutting carbon emissions from existing homes.
"Collectively our homes account for around 25% of the country's carbon emissions - so it's vital we all work together to lower that figure.
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"Clearly housing associations - which manage two million homes in England - will have a vital role to play in achieving this target.
"We look forward to meeting with the Government on Friday to discuss the ambition and what funding can be put in place to help us reach this."
Mr Orr however said ministers were in danger of sending out mixed messages on environmental standards when it came to the building of new homes.
He warned the Government could miss its target of making all new homes zero carbon by 2016 - because tough new eco standards introduced last year do not currently apply to private builders.
Around 92% of housing association new homes are already meeting minimum sustainable standards of emitting 25% less carbon, while only 2% of new homes built by private developers do so.
Mr Orr said: "We hope the Government has learnt from the mistakes it made last year when it introduced two separate timetables for meeting new environmental building standards.
"The construction industry is currently being sent mixed messages. On one hand we are being told that existing homes need to cut the amount of energy they use, but on the other hand private developers are still building new homes to nothing more than minimum energy standards.
"If the Government is serious about climate change it should raise the minimum energy standards of new homes across the industry as soon as possible."
(CD/JM)
