Several people were trapped after a fire broke out inside a house in Coronation Crescent at around 8pm on Friday (April 8).
A woman and two children were rescued from the inferno by firefighters.
The two children – a girl aged three and a boy aged five – remained in hospital in “critical condition” on Monday (April 11).
Police said their next of kin were with them in hospital and were being supported by specially-trained officers.
The woman, aged in her 20s, suffered injuries which were not believed to be life-threatening.
A 24-year-old man who was arrested on suspicion of arson with intent to endanger life was initially released under investigation pending further enquiries.
He was later released with no further action.
Det Chief Insp Graham Hill, of the Force Major Investigation Team, said: “He has been eliminated from our enquiries and we are not currently looking for anybody else in connection with the investigation.
“Our enquiries into the cause of the fire are continuing, however, at this stage of the investigation there is no evidence to suggest that the cause of the fire is suspicious.
“I would urge people not to speculate and we will update you in due course.”
Officers said a joint investigation between police and the fire service was continuing.
Anybody with information is asked to get in touch on 101, quoting log 1305 of April 8th.