Kevin Curley, chief executive of the National Association for Voluntary and Community Action, made the appeal in a meeting with Mr Stoker.
'NAVCA and our members have made clear that we believe that John Stoker's first task should be getting those reluctant local authorities into line.'
The Compact is the agreement between government and the voluntary and community sector in England to improve their relationship for mutual advantage. It sets out the statement of intent to work in partnership and is supported by five codes: funding and procurement, community groups, BME groups, volunteers and consultation.
Local Compacts inform joint working at a local level, from police working with the community sector to tackle anti-social behaviour to social services improving their contracting with social care organisations.
Mr Curley said NAVCA was also calling on the Audit Commission to strengthen its local inspection focus to consider the quality of local authorities' engagement and partnership working with the local VCS.
A survey of NAVCA members shows just over half want the Compact Commissioner to take robust action against local authorities that breach the Compact, while just under half believe the Commissioner should act as an 'honest broker' between the two sectors.
NAVCA's 360 members work with 140,000 local community groups and voluntary organisations that provide services, regenerate neighbourhoods, increase volunteering and tackle discrimination, in partnership with local public bodies. It was previously known as NACVS.