The findings were revealed in a Local Government Association survey, which asked councils in England to give their views on regional governance.
Just 35% felt directly elected regional assemblies would lead to a 'significant'
devolution of power from central government.
LGA chair Sir Jeremy Beecham (Lab) underlined the association's stance that power must be cascaded down from Whitehall and not taken from local government if regional assemblies are established.
'[We will hold the government to account] to ensure local government is the front-line deliverer of many of the proposed regional strategies and to ensure communities have proper representation,' Sir Jeremy said.
But the results showed a majority of councils - between 54% and 63% - believe the proposal would improve effectiveness and accountability, give regions a stronger voice at Westminster and boost economic conditions.
Some councils reacted positively to government proposals to strengthen government offices for the regions with extra responsibilities in monitoring crime and drug reduction.
The outlook was not as bright when it came to the perceptions councils had of their own role in areas like emergency planning, community cohesion and e-government. The number believing they would play a 'successful role' in these areas hovered around the 50% mark.
While only 43% of councils reported having at least a good relationship with their regional assembly, nearly three-quarters said their assembly kept them at least 'fairly well informed'.