The Lord Mayor of Dublin Oisin Quinn is calling on the Government to proceed with a plebiscite on a directly elected mayor after the plan was ended by Fingal councillors.
Sixteen councillors voted against the proposal while six voted in favour and there were two abstentions.
All four councils in Dublin had to support the plebiscite for it to go ahead.
Dublin City, South Dublin and Dun Laoghaire Rathdown councils have all voted overwhelmingly in favour of the motion.
The capital's current Lord Mayor Quinn has said Dubliners should still be allowed elect their own mayor despite the opposition in Fingal.