Voters in Limerick will have the chance to select a directly elected mayor by 2022 after a plebiscite passed by 52.4% to 47.6%.
However, voters in Cork and Waterford narrowly rejected the idea meaning the current local authority structures will remain in place.
The Government had pledged to bring legislative proposals to the Oireachtas within two years for a directly elected mayor with executive functions if the plebiscites passed.
The Department of Local Government said the result of the plebiscite in one administrative area would have no consequence on the other administrative areas
The Programme for Government had committed to holding plebiscites for directly elected mayors in Dublin, Cork, Limerick, Galway and Waterford as the five largest cities in the National Planning Framework.
However, because Dublin is currently made up of four local authority areas, the issue is to be referred to a Citizens' Assembly.
The Government said that due to the complexities of local government in county Dublin and the Dublin metropolitan area, it needed to allow space for detailed and informed public discourse on the matter.
Voters in Galway will also have to wait until the city and county councils are merged before being asked their views in 2021.
The Minister of State for Local Government and Electoral Reform, John Paul Phelan said he noted the decision and re-iterated the government’s pledge to legislate for the position by 2022 in Limerick.
"The mayor of Limerick is going to be answerable to the people of Limerick and will drive development and growth in the city, county and wider region," he said.
Limerick Senator Maria Byrne said the move would help bring about balanced regional development.