The vote was held at a meeting on Saturday
Housing Minister Eoghan Murphy has expressed his full confidence in Sean Hogan, National Director for Fire and Emergency Management, and Patrick Fleming, Chief Fire Officer at Dublin Fire Brigade.
It comes after SIPTU members of Dublin Fire Brigade voted no confidence in both men on Saturday.
The no confidence motions were taken at an emergency meeting in the wake of a high-rise fire in Ballymun last Wednesday.
SIPTU Sector Organiser, Brendan O'Brien, said: "Policy makers and management have had many opportunities to resolve the issues raised by our members.
"However, we believe no satisfactory improvements have been made despite SIPTU representatives continually raising health and safety concerns."
SIPTU Dublin Fire Brigade convenor, Shane McGill, added: "These votes of no confidence come directly from our members. They are front line firefighters working in fire stations and control rooms across Dublin city and county and they have had enough.
“These members are not only disillusioned and angry with the policies and the direction management has taken so far, but how they have continually turned a blind eye to the concerns of operational staff and the representations made to them about training, safety, safe systems of work and exposure to risk."
In response, Minister Murphy said: "People will be surprised at this evening’s statement from SIPTU.
"Anyone who has seen the role that Sean Hogan has played in leading the country’s response to many national emergencies, most recently in relation to snow storm Emma at the beginning of this month, a role that I have witnessed first-hand myself, will recognise Sean’s extraordinary leadership ability, his sound judgement and sheer dedication to public service and public safety.
"Pat Fleming and Sean Hogan have made an extraordinary contribution to developing and implementing fire safety policy in their various roles in leading local authority delivered fire services in this country.
"This is what makes it hard to believe that SIPTU would issue a statement of the kind we saw today.
He also highlighted the role that Mr Fleming and Mr Hogan are playing in leading a fundamental change in how we manage fire risk in Ireland.
This change of emphasis, he said, is in line with international best practice of preventing and building fire protection into buildings - as well as having fire brigade response.
Mr Murphy also said that fire safety policy, which has resulted in declining numbers of fires, as well as having smoke alarms in over 90% of households, is not a threat to our operational fire service.