Fingal County Council has voted against letting the public decide on whether there should be a directly-elected Mayor of Dublin.
The votes were 16 against, six in favour and two abstentions.
The meeting voted in favour of having a referendum at a later date under amended legislation to allow more time for debate.
The meeting agreed a motion to allow Dublin city to elect its own mayor.
The agreement of all four Dublin local authorities was required for a plebiscite to go ahead in May.
Dublin South Council this afternoon voted in favour of holding a plebiscite, with 19 votes in favour, three opposed, one abstention, and three absentees.
Last week councillors in Dublin City voted overwhelmingly in favour of allowing a plebiscite on the idea of a directly elected mayor to be held on the same day as the European and Local elections.
This evening, Dún Laoghaire Rathdown councillors voted overwhelmingly in favour of a Dublin Mayor plebiscite.
All 23 councillors present voted in favour.
The Mayor of Fingal, Fine Gael Cllr Kieran Dennison, said the current proposal would be a costly addition to local government bureaucracy.
A number of councillors also argued that Fingal would lose out by having a Mayor based in Dublin city centre.
Labour Cllr Tom Kelleher said Fingal is probably the most successful local authority in the country and competes with Dublin city for investment.
Socialist Party Cllr Ruth Coppinger said a directly-elected Mayor would involve too much centralisation of power and take power away from councillors.
She also said a position would govern one third of the country and pose too much risk of corruption.
But other councillors said they could not vote against letting the public have their say.
Fianna Fáil Cllr David McGuinness pointed out that both Fine Gael and Labour election manifestos had supported a Dublin Mayor.
The Dublin Chamber of Commerce, which has been campaigning for a mayor for Dublin, says if this opportunity is lost there will not be another for decades.