The Welsh Local Government Association said there should be a distinct 'Welsh way', called the Wales Programme for Improvement, which would bury the bad reputation of best value.
But the Assembly has sent a letter to all councils saying they must continue to comply with best value.
The Welsh Assembly's head of local government modernisation Kate Cassidy said the Assembly does not have the power to scrap best value.
Association director Sandy Blair and the association's best value spokesman Russell Goodway (Lab) met Welsh local government minister Edwina Hart and representatives from the Audit Commission to discuss the future of best value.
Meanwhile the Audit Commission issued a report saying Welsh councils' best value performance plans have improved dramatically since last year.
No councils in Wales received adverse qualification from the commission compared to the third that received the damning verdict last year.
The report says: 'Plans are of a higher standard than last year, showing authorities are making progress.'
But Mr Goodway dismissed the commission's claims Welsh councils are adapting to best value.
He said: 'Our criticism is about processes and whether they have the right people. The fact councils have written better reports doesn't reflect any real change. They are trying to give a more encouraging picture, but confidence has been destroyed.
'There needs to be a fundamental change to the system. It is teetering on the brink. Best value has been hi-jacked by academics and civil servants, and we need to get back to the original meaning.'