Philip and Kim English were killed in the fire in Waterford shortly after 5am on Tuesday.
Two children, named Callum and Jayden, also died, while two more children with critical injuries were taken to hospital in Dublin.
On Thursday, police arrested a man in his 20s and a woman in her 30s over the incident.
Police believe the blaze was started deliberately and have begun a murder investigation.
A post-mortem examination on Mr and Mrs English and their sons have been completed but the results are not being released for “operational reasons”.
Gardai have repeated their appeal for information which took place on Birch Avenue, Birchwood.
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