Acevo regards the meeting as a breakthrough in its drive to remove obstacles to a greater sector contribution to public service provision.
Stephen Bubb, chief executive of Acevo, said he would be making the case for longer contracts for the sector, which could bring more access to private capital.
"The Department of Work and Pensions is already talking about five-year contracts, and there's a case for 10 or 15 years if capital is involved, as in the building of residential homes."
He said he would also press for better government co-ordination of voluntary sector concerns, for which there is no cross-cutting ministerial committee.
One idea would be to replicate in other departments the recently formed Department of Health taskforce on better access for the voluntary sector.
"Another possibility is an implementation team, perhaps given the task of taking the agenda forward and reporting in a year," he added.
The meeting with Blair, which was due to take place yesterday, comes as ministers have endorsed a greater role for the sector, but frustration mounts over practical questions such as contracts, full cost recovery and VAT.
Ahead of the meeting, Blair said: "We will work with the sector on an action plan for change."
Other ministers due to take part were Ivan Lewis (Treasury), Liam Byrne (Health) and Hazel Blears (Home Office). The Acevo delegation included John Low of RNID and Barbara Frost of Water Aid.
- See News, page 3.