The Health Minister has rejected calls in the Assembly for a public inquiry into how Arthur McElhill set fire to his Omagh home and killed his family.
Mr McElhill's partner Lorraine McGovern and their five children died in the blaze in November 2007.
Michael McGimpsey told MLAs there were no substantive grounds for the inquiry and warned it could be distressing for relatives.
Supporting the Assembly's call, Sinn Fein member Michelle O'Neill said: "We also believe that again all the other agencies need to take responsibility here. We need to minimise risk."
"Nobody can say for sure that an event like this will never be repeated but as long as we are confident that we have taken forward all the things that we can to ensure that the best practices are in place and that people work together more efficiently."
McElhill, from Lammy Crescent, Omagh, Co Tyrone, burned the house down because his partner, Lorraine McGovern, threatened to leave him, an inquest in December concluded.
On the opening day of the inquest forensic investigators said that the fire had been started when someone who was inside the house set light to a mixture of petrol and white spirits which had been poured in the hall.
A court clerk reading a statement from a Fire Service commander struggled with emotion as she delivered his description of searching the house as the fire came under control.
First he found the bodies of two adults, then the children and finally a baby in a cot.
The children were Caroline, 13; Sean, 7; Bellina, 4; Clodagh, 19 months and James, nine months.
'Distress'
The Assembly voted to call on the minister to seek the agreement of Northern Ireland Secretary Shaun Woodward for a public inquiry.
Mr McGimpsey said he would write to the Office of the First Minister and Deputy First Minister (OFMDFM) asking them to raise the matter with the Northern Ireland Office.
However, he said a review had already identified failings by the social services.
"In light of this I am therefore of the view that there are no substantive grounds arising from those areas for which I have responsibility for the holding of a public inquiry into this tragedy," he said.
"We all need to be mindful of the distressing effects that any public inquiry would have on both families given the ongoing significant media interest in this case."
He said budgets were already under pressure but added if it was believed unanswered questions could be addressed then he would support a public probe.
Mr McGimpsey said health and social services faced a £113m cut even though child and family services were underresourced by 30% compared to other parts of the UK.
Over the past five years the number of children referred to social services has increased by nearly a third.
"Everyone here knows that I have been warning the Assembly for the past two and a half years about the dangers of underfunding health and social care services," he added.
© Press Association