Eight-year-old twins Austin and Luke Riggi and their five-year-old sister Cecilia were discovered in an Edinburgh townhouse on August 4 following reports of an explosion.
Their mother, Theresa Riggi, 46, who is being treated in hospital after apparently falling from a second-floor balcony, has been charged with their murder.
Prayers were said for the children at St Mary's Cathedral in Aberdeen, where they lived until shortly before their deaths.
The family asked mourners to make donations to the Reverend Gordon Trust Orphan Fund, instead of flowers.
In a statement, Peter Moran, Bishop of Aberdeen, said: "Everybody is very shocked and distressed by the deaths of these three children, and I'm particularly distressed because they worshipped here. In fact the twins made their first Communion here just in the spring of this year.
"I'm pleased that they have their extended family with them. These are people of great faith. So the church is a family too and they have turned to the church for comfort.
"And when we think of the children themselves we trust in God, we ask Him to take them into His care and take them home. And all the more so because they are so young and innocent.
"And then of course, a quiet word. A quiet prayer for the mother of the children because God is the only one who knows and can see into her troubled heart."
Bells tolled steadily shortly before 11am as mourners began to arrive at the city centre cathedral.
The children's father, Pasquale Riggi, wearing dark glasses, was among the last to enter for the Roman Catholic Mass.
During the service, Bishop Moran said: "The unthinkable has happened, and the unbearable has to be borne.
"We are here, family, friends, work colleagues, clergy, because we don't want Pasquale, his parents and his parents-in-law to carry that burden alone, to suffer alone in their terrible loss."
Three tributes were given, including one from Mr Riggi's sister, Lillian Mancinelli, and her husband, Joe.
Hymns and prayers were chosen by the family.
Bishop Moran's homily described the comfort that has been given to the grief-stricken family.
Candles were lit for the children and bread, wine and water was brought forward.