Officers say the man, detained on Friday night on suspicion of arson with intent to endanger life, has been freed from custody "under investigation."
The blaze in a terraced house in Coronation Crescent, Frenchwood happened just before 8pm on Friday.
The two children - a girl aged three and a boy aged five - and their mother were rescued from the inferno by firefighters.
They are said to be in a critical condition in hospital. The woman, in her twenties, suffered injuries which are not thought to be life-threatening.
A police spokesperson said relatives of the children are with them in hospital and are being supported by specially-trained officers.
A joint investigation with the fire service was launched and at this time the fire is still being treated as unexplained.
"A 24-year-old man arrested on suspicion of arson with intent to endanger life has now been released under investigation while enquiries continue.
"We are continuing to ask anybody with information about the incident to get in touch."
Locals who tried to rescue the woman and her children spoke later of hearing the mother screaming for help at a bedroom window.
Demi-Lee Carroll and boyfriend Hayden Wolstencroft dashed from a nearby shop when the alarm was raised.
"I was in the street trying to get the mum to drop the kids down to me," said Demi-Lee. "She tried but she couldn't do it.
"Then she jumped out herself. She told me she was pregnant and I rushed to get her some water and sit her down.”
Hayden added: "You could see flames and there was no way for the mum and babies to get out.
"The woman was hanging from her window screaming for help. I tried to get closer, but the flames were already smothering the house."
Builder Gordon Simpson, who was visiting the couple from Kendal, was treated in hospital for smoke inhalation after he tried to get into the house but was driven back.
"The smoke was unreal when we got to the back of the house," he said. "I smashed in the window and pulled back the curtains. I was screaming, 'come here', but I don't know if they could understand or hear me.
"Everything was black inside. I was overwhelmed by the smoke."
DCI Graham Hill, of the Force Major Investigation Team, said: “Sadly the two children are still in hospital with life-threatening injuries, and we continue to keep them and their family in our thoughts at this awful time.
“A joint investigation with Lancashire Fire and Rescue Service is ongoing and the fire is being treated as unexplained while we establish a cause.
“We continue to ask if you have any information about the incident, and have not yet spoken to police, that you contact us as soon as possible.”
Anybody with information is asked to get in touch on 101, quoting log 1305 of April 8.