Amy Smith, 17, her six-month-old daughter Ruby-Grace Gaunt and friend Edward Green, also 17, were killed by the blaze on North Street at around 4am.
In a statement the Anglican Diocese of Derby said it had opened books of condolence at St John's Church, Cromford Road, Aldercar and St Andrew's Church, Station Road.
The Church said people were invited to pray, sign the books and donate money to the families affected by the tragedy.
Three men have been arrested on suspicion of murder following the fire.
The baby's father, Shaun Gaunt, and two other people are believed to have also been caught up in the blaze.
Derbyshire Police said: "A 17-year-old from Long Eaton, and a 21-year-old and a 43-year-old from Sandiacre, were all arrested late last night on suspicion of murder.
"The three men remain in custody this morning and are being questioned.
"Officers are still working closely with Derbyshire Fire and Rescue Service to ascertain the cause of the fire, which is still unknown at this stage."
Assistant Chief Constable Martyn Bates said: "The cause of the fire is still unknown and the possibility that it was started deliberately is just one of many lines of inquiry we are pursuing at this time.
"These arrests do not mark the end of the investigation, far from it. I would still urge anyone with information to come forward and speak to us."
