"We can confirm 10 fatalities now," an Irish police spokesman told AFP, but he could not say how many were children.
Members of two related families are believed to have died, including a baby as young as six months old.
"Unfortunately a husband and wife, their four sons and baby daughter and other relations are lost," said Irish Prime Minister Enda Kenny.
"It's such an unspeakable tragedy to have an entire family wiped out in a horrific inferno," he added.
Dublin Fire Service said it was too early to establish the cause of the fire in the south Dublin suburb of Carrickmines, which is about 16 kilometres (10 miles) from the city centre.
A police source said the fire did not appear suspicious but that a forensic investigation was under way to discover the cause and how it spread.
Emergency services were alerted shortly after 0300 GMT.
Irish President Michael D Higgins described the incident as a "dreadful tragedy".
Local councillor Peter O'Brien said: "People went to bed on a Friday night looking forward to the weekend and never woke up".
"That's a hard thing to get your head around," he told AFP at the scene.
The Southside Traveller Action Group, which offers support to travellers in the area, said the community was "in a state of shock at the devastating" events.
People left homeless by the fire will be accommodated by authorities in Dublin, the group said in a statement.
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