Cheryl Korbel, whose nine-year-old daughter was shot in their home in Dovecot, Liverpool, paid tribute to her “little shadow”.
Ms Korbel, 46, said she hoped whoever was responsible for the killing would come forward.
In an appeal released by Merseyside Police, she said: “You know you’ve done wrong, so you need to own up.
“Like I taught my kids, you do something wrong, you own up to it.
“If anyone is hiding these guns they need to speak up because they need to be off the streets.
“No one, no one at all should have to go through this.”
Wearing a cast on her wrist after being injured during the shooting, Ms Korbel said the family had been planning days out and a trip to buy Olivia’s new school uniform before she died.
She said: “I didn’t get that chance to go and get her school uniform.
“But I’ll keep going, for Liv.”
She broke down in tears as she described how her daughter would never stop talking and said: “That’s what I miss the most, because I can’t hear her talk.”
Olivia’s dad, John Francis Pratt, also paid tribute to his daughter and called for anyone with information on her death to come forward.
In a statement, Mr Pratt and his wider family said: “We don’t want another child to lose their life in such horrendous circumstances and we don’t want to see another family suffer like we are suffering now.
“Olivia’s death cannot be in vain and we want people to feel safe and be safe, that can only happen if we all come together and make sure there is no place for guns, or those who use guns on our streets or in our communities.”
Olivia Pratt-Korbel's mum issued an appeal through Merseyside Police
Merseyside Police
A 34-year-old man from Liverpool arrested on suspicion of murder and attempted murder remains in custody after police were granted an extension to continue questioning him.
Three other men have been arrested on suspicion of assisting an offender.
Olivia was shot in her home when a gunman chased convicted burglar Joseph Nee into the property at about 10pm on August 22.
A post-mortem examination found the medical cause of her death was a gunshot wound to the chest.
Cheryl Korbel described daughter Olivia as her 'little shadow'
Merseyside Police
Olivia Pratt-Korbel was fatally shot at her home in Knotty Ash, Liverpool
Family Handout