He told the Welsh Local Government Association's annual conference on Friday that the national assembly - being set up next year - had the potential to help create a central/local government partnership second to none in the UK in terms of delivering results.
'There is no reason at all why, between us, we cannot make local government in Wales the envy of that in the rest of the UK, judged by the quality of the services provided, the efficiency with which they are delivered and the conduct of elected members and employees alike,' he said.
'I want Wales to be the place that people turn to when they want models of best practice.'
'Though the government will decide the size of the budget available to the assembly, it will be the assembly which will have the power to decide what proportion to allocate to local government and the way in which this share is split between individual councils - though, as now, hopefully on the basis of a consensus approach.'
Mr Griffiths said the assembly would set up a Partnership Council made up of representatives of local government and the assembly.
'The council - unique within the UK - will enable local authorities to contribute directly to assembly thinking on the full range of its functions, including the activities of the quangos and the NHS,' he said.
The assembly would also prepare a scheme to sustain and promote local government in Wales, he said.
'The scheme could outline the vision for local government in Wales and set out as broadly or in as much detail as the Partnership Council advises how working together the assembly and local government will achieve it.'
Mr Griffiths emphasised that the relationship between local government and the assembly would not operate only through the Partnership Council.
'The assembly will be open to local government influence at a variety of levels,' he said. 'Local authorities will be able to make an input to the regional committees which the assembly will set up. These will enable local authorities to examine the impact of the assembly's policies and the operation of its agencies, and to lobby about their regions' needs.
'Councils will also be able to deal directly with the whole range of Assembly Secretaries and with subject committees.'
Mr Griffiths said that in return for a greater say in the assembly's policy making and, in particular, the way in which councils would be regulated, the assembly was likely to expect higher standards of performance from councils.
The guiding principle would be for both partners to be aware of the other's viewpoints on important matters of the day.
'Better decisions on both sides will be made on the basis of negotiation and compromise if these understandings are in place,' he said.
Turning to Welsh Office plans for modernising local government, Mr Griffiths said the period of consultation on the proposals was drawing to an end.
Officials were already beginning to analyse the responses to the seven consultation papers, and the aim was to publish a White Paper on local government in Wales by the end of July.
Mr Griffiths said that although local authorities had not signed up to every dot and comma of the proposals, Welsh councils had overwhelmingly given their backing to the key policy objectives and the main means of achieving them.
'I have no doubt whatsoever that we have the skill, the political commitment and the opportunity to grasp this once in a generation opportunity to renew local democracy in Wales and to take it to levels previously undreamt of,' he concluded.