Video report by ITV Granada Reports' journalist Rachel Townsend
Merseyside Police have named the child as Olivia Pratt-Korbel, and say her family are "absolutely devastated, inconsolable and heartbroken" following the incident in Kingsheath Avenue, Dovecot, on Monday night.
Chief Constable Serena Kennedy said a 35-year-old man was being chased by a person with a gun, who forced entry into the house and opened fire with "complete disregard", hitting Olivia.
The nine-year-old child was taken to Alder Hey hospital in a critical condition, where she later died.
Two other people - including Olivia's mother, Cheryl - are in hospital with gunshot wounds.
Chief Constable Serena Kennedy speaks to the media after a nine-year-old girl was fatally shot in Dovecot
Police say at around 10pm two men were walking along Kingsheath Avenue and were approached by a lone person wearing a black, padded jacket, a black balaclava and black gloves.
They were approximately 5 foot 7 inches tall, of slim build and carrying a handgun.
The force says shots were fired at the men who then ran away.
Olivia's mother is said to have heard the commotion outside and opened the door to see what was going on.
One of the men is then thought to have forced his way into the property, with the armed person said to have put their hand through the open door.
Olivia's mum is believed to have tried to close the door and stop the people entering, but the gunman open fire, hitting both Olivia and her mother.
The man who had been chased "suffered a number of gunshots to his upper body" and, whilst Olivia lay dying, was picked up by his friends who took him to hospital.
The car that took him to hospital - a black Audi - has been seized by police.
Merseyside Police Chief Constable, Serena Kennedy, said: "I know that the murder of Olivia has rocked our communities, who are quite rightly upset and outraged that such an abhorrent crime has occurred here on the streets of Merseyside.
"The people of Liverpool and Merseyside are known for their compassion and pulling together in times of crisis, and I know that our communities, people are wanting to help the family in any way possible.
"This is not the time for anyone who knows who’s responsible for this shooting to remain tight-lipped.
"It is time for our communities to come together with us and make Merseyside a place where the use of guns on our streets is totally unacceptable, and those who use them are held to account."
Watch the full police press conference
Olivia was a pupil at St Margaret Mary's Catholic Junior School in Huyton.
Headteacher, Rebecca Wilkinson, has described her as having a "beautiful smile, a lovely sense of humour and a bubbly personality".
She said: "Our school community is devastated at the sad loss of Olivia. We are in shock and disbelief at such tragic news.
"Olivia was a much loved member of our school. She had a beautiful smile, a lovely sense of humour, and a bubbly personality.
"She was kind-hearted and would go out of her way to help others. She loved to perform and recently participated in the school production of The Wizard of Oz.
"Olivia will be missed greatly by staff and children at our school. Our thoughts and prayers are with her family and friends at this extremely sad time."
A murder investigation has been launched and a huge police presence remains at the scene, with residents have described the incident as "devastating".
Anyone with information is asked to DM @MerPolCC or call @CrimestoppersUK on 0800 555 111 quoting log 1083 of 22 August.
The killing came 15 years to the day after 11-year-old Rhys Jones was shot dead in Croxteth.
The mayor of Liverpool Joanne Anderson has said the nine-year-old's murder is an "appalling act of evil".
She said: "15 years to the day that Rhys Jones was murdered, another innocent child of our city becomes a victim to gun crime.
"Has nothing been learned? Enough is enough. If you know something, you must come forward. Guns have no place in our communities."
The Prime Minister Boris Johnson offered his condolences to the family and said he has ensured Merseyside Police "get whatever they need to catch those responsible."
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