In a joint statement, they said: "We welcome the First Minister setting out his vision for the next stage of devolution in Wales. For us, the important question is not simply where power sits, but what we can achieve with it for the people and communities we serve.
"This fits in with the Prime Minister’s ambitions on devolution and rewiring Britain. We believe devolution should not stop at Cardiff Bay, and all three levels of Government in Wales have an opportunity to move forwards together, devolving power closer to the people.
"Wales should learn from experience elsewhere, but we should not simply import somebody else’s model. We have our own institutions, traditions and economic geography. We have the opportunity to develop a 'Welsh Way', connecting national ambition with regional scale and the knowledge and democratic leadership of local government.
"Given the announcements made by the PM in recent weeks about increased innovation powers to English Combined Authorities and early signs of regional economic empowerment in Scotland, the opportunity is now and the pace matters. We will work positively with the Welsh Government to ensure the process of designing the future, does not delay the opportunity to deliver it.
WLGA Leader, Cllr Anthony Hunt, added: "Regional working can play an important part in that. It brings together councils, businesses, universities, public bodies and investors at a scale that can unlock opportunities no single organisation can deliver alone. But regionalism should strengthen local government, not weaken or compete with it.
"The prize is a stronger Welsh economy, better connectivity, more investment, innovation and good, high-skilled jobs across all parts of Wales. Ultimately, however, the test of further devolution is delivery. People need to see and feel the difference in their communities, public services, local economies and pay packets. That requires clear priorities, strong partnerships and the flexibility to act. National leadership, regional collaboration and strong local government should reinforce one another.
"If we get that relationship right, Wales has an opportunity to create something distinctive: a 'Welsh Way' built around partnership rather than competition, bringing decisions closer to people and turning our shared ambitions into practical results."