The housing estate is just off the Killure Road, about 3km (1.8 miles) outside Waterford city centre.
Sinn Féin TD (member of the Irish Parliament) David Cullinane said he knew the family and said his heart went out to their relatives.
“I’m just utterly heartbroken,” Cullinane said.
“There is such devastation in the housing estate itself but also in the wider community in Waterford city.”
The Bishop of Waterford and Lismore, Alphonsus Cullinan, described it as an “unspeakable tragedy” which had shocked the entire city.
He said the Catholic Church would “reach out as best we can” to help those affected and the parish priest would likely call to offer support.
The bishop said neighbours living in the estate would also have been affected by the incident but he believed they would rally round to help the family.
The mayor of the Waterford Metropolitan District, Lola O’Sullivan, urged people not to speculate about the cause of the fire.
“It upsets me no end to see people commenting on social media about something that they don’t have firm facts on,” she said.
Waterford City and County Council has opened a support hub for people who have been affected by the fire.
It said facilities and refreshments were available at Butler Community Centre in St John’s Park.