Residents in Newcastle have set up a GoFundMe campaign to support the McGinley family.
It has been established by a member of Newcastle Community, along with the ReNewcastle Community Group.
They say they are in touch with the family, who are aware of the campaign and are "very thankful".
As of 4.30pm today, more than €5,700 euro has been raised.
According to the group, Andrew McGinley's employer SODEXO is covering the funeral costs.
Earlier - 'Every breath is a struggle': Father speaks of 'devastation' after discovering his children were dead
'There are no words, only devastation.' These were the words of heartbroken Andrew McGinley, whose three young children were found dead at the family home last Friday evening.
In a statement issued this morning, Mr McGinley also released a family photograph, including his wife, Deirdre Morley.
She remains in hospital after being found in a collapsed state at the time her husband discovered the children's bodies at their home in Newcastle, west Dublin at around 7.45pm.
The results of toxicology tests on Conor, aged nine, Darragh, aged seven, and their little sister, Carla, aged three, are expected later in the week.
Together with inconclusive findings from the post mortem, gardaí hope the results will explain how the children died.
In a moving statement issued through Garda HQ, Mr McGinley said: "There are no words. There is only devastation, grief and anguish. Every breath is a struggle."
“Conor, Darragh and Carla are adored. They all had beautiful, bright futures ahead of them with family, friends and a community who love them.”
He had this message to parents:
“To all parents, cuddle your children whenever you get a chance, tell them how much you love them as often as you can, spend every spare minute with them reading, playing and enjoying their wonderfulness.”
He added: “The future has now become our enemy but we will battle it every day to keep the memory of Conor, Darragh and Carla alive. Andrew.”
Accompanying his statement, the father released a family photograph, comprising himself, his three children and his wife.
Ms Morley had been found in a disorientated state near her home by a taxi driver at around 7.30pm. The driver brought her home, but her condition deteriorated on the way and he had to ring 999.
A garda patrol was in the area on a separate matter when they saw ambulance staff tending to a person outside a house and went to see if any assistance was needed.
By that stage, Mr McGinley had arrived home. It is understood that when he saw his wife being cared for outside the house he went inside to see if his children were okay.
When gardaí heard the father's anguish they went into the house, followed by paramedics.
It is thought one of the children was downstairs and the two others were upstairs.
It is understood two notes were found inside the house, one of them inside the door, asking the reader to ring 999 and not to go upstairs. Both notes are being forensically examined.
The Technical Bureau has conducted a detailed examination of the house.
Ms Morley, a nurse, was described as being in a critical condition when she was brought to Tallaght Hospital. She is thought to have stabilised over the weekend, but is still in a serious condition.
Sources said doctors will need to be satisfied that she is both medically and psychologically able to speak to gardaí before giving detectives the all-clear.
The children's bodies have not yet been released to their father.
'Cuddle your children whenever you get a chance': Andrew McGinley describes grief after childrens' death
The father of three children who were found dead in a house in Dublin last week has described his "devastation" following their deaths.
The bodies of nine-year-old Conor McGinley, his brother Darragh who was seven, and their sister Carla, who was three, were discovered in a house in Newcastle on Friday evening.
Post-mortem examinations were carried out on their bodies but gardaí say they will not be releasing the results for operational purposes.
Gardaí say it could be up to a week before the results of toxicology tests are known.
Andrew McGinley, father of Conor, Darragh and Carla, has urged parents to spend more time with their children.
"There are no words. There is only devastation, grief and anguish. Every breath is a struggle," he said in a statement released through the Garda press office.
"Conor, Darragh and Carla are adored. They all had beautiful, bright futures ahead of them with family, friends and a community who love them.
"To all parents, cuddle your children whenever you get a chance, tell them how much you love them as often as you can, spend every spare minute with them reading, playing and enjoying their wonderfulness.
The future has now become our enemy but we will battle it every day to keep the memory of Conor, Darragh and Carla alive.
Gardaí are still waiting to interview the mother of the three children, who is aged in her 40s and currently in a serious condition in hospital.
A family liaison officer had been appointed and is in contact with the father and the extended family.