The two bodies are drawing up a set of proposals about how the paper, Strong and Prosperous Communities, can be put into practice at a local level.
The paper, published last week by Ruth Kelly, Secretary of State for Communities and Local Government, recommends devolving more power to local government and giving local people a greater say in how their communities are run.
It contains an entire chapter on the third sector and the role it can play in achieving that goal - a step that has been warmly welcomed by voluntary sector leaders.
"The white paper's chapter on the third sector is symbolic in itself," said Stephen Bubb, chief executive of Acevo. "Normally we'd be lucky to get a couple of paragraphs. I think they're realising we're now part of the deal."
Bubb called on the sector to respond responsibly to the Government's proposals. "It's a historic document, but we have to work to make it a reality," he said. "That requires us to look at our own house, stop whingeing and get on with the practicality. There's a responsibility for us to go to local authorities and say 'here's the white paper, what are you going to do about it?'"
Acevo and the LGA will stage a conference in December to discuss how local services can be made more responsive to communities.
The NCVO reacted to the white paper by asking the Government to provide communities with the relevant skills and resources they need to play a greater part in local governance. It would like to see training for both voluntary and statutory organisations so they understand their respective roles.
One initiative that has met with particular enthusiasm from the sector is the creation of a fund to refurbish local council buildings so they can be taken over by voluntary organisations.
"This is a welcome recognition that many buildings in council ownership could be put to far better use by enterprising community organisations," said Steve Wyler, director of the Development Trusts Association. Wyler hopes the white paper signals the end of what he calls a "narrow municipalism that has held back community development for a generation".