Jake Davison, who killed five people, including a young girl, in Plymouth was a licensed firearms holder, police have revealed.
The 22-year-old shot two women, two men and the three-year-old girl in a deadly six-minute spree in the Keyham area of the city on Thursday evening.
Police said the incident, the worst mass shooting in Britain since 2010, was not terror-related.
In online videos Davison spoke of being "beaten down" and "defeated by life".
Emergency services were called to Biddick Drive shortly after 18:00 BST on Thursday. Five people, including Davison, died at the scene and one died later in hospital.
Devon and Cornwall Police Chief Constable Shaun Sawyer said Davison was a firearms licence holder.
He said the weapon used in the shooting had been described by witnesses as a "pump action shotgun" but police were not confirming that at this stage.
Mr Sawyer said a firearm had been recovered from the scene and officers were not looking for anyone else in connection with the incident.
He said: "We believe we have an incident that is domestically related, that has spilled into the street and seen several people in Plymouth losing their lives in extraordinarily tragic circumstances."
The police received calls to an address on Biddick Drive at 18:11 BST and armed and unarmed officers arrived with six minutes.
Mr Sawyer said "multiple shots have been fired from a firearm during that six-minute-or-so period".
He said Davison murdered a 51-year-old woman who was known to him, with police believing there may be a familial relationship.
He then went out on to the street, where "he immediately shot and killed a very young girl. He also shot and killed the male relative of that girl", who was aged 43.
Davison then shot another woman, 53, and a man, 33, on Biddick Drive who remain in hospital with injuries "not thought to be life-threatening".
He next went into a park, where he shot a 59-year-old man who died at the scene, and then moved to Henderson Place where he shot a woman, 66, who later died at Derriford Hospital.
"Eyewitnesses have told us that then Mr Davison turned the gun on himself taking his own life," said Mr Sawyer.
The police are working at 13 scenes and said they would examine Davison's computer hard drive and social media posts as part of the investigation.
Mr Sawyer said "no motive" had been identified at present.
The Independent Office for Police Conduct (IOPC) said it had received a mandatory referral from the Devon and Cornwall force.
The referral was in relation to the shooting as well as prior police contact with Davison, including the force's role and actions regarding firearms licensing.
Gun laws in the UK are sometimes described as some of the strictest in the world and a certificate issued by the police is needed to possess, buy or acquire a firearm or shotgun, and ammunition.
In the online videos Davison said he was socially isolated, struggled to meet women and made references to "incels" - the misogynistic online groups of "involuntary celibate" men, who blame women for their sexual failings and who have been linked to a number of violent acts around the world.
Signing off on an 11-minute video, which appears to be the last he posted, Davison said: "I know it's a movie but I like to think sometimes I'm the Terminator or something. Despite reaching almost total system failure he keeps trying to accomplish his mission."
Posting on Reddit three weeks ago, Davison, who claimed to have got a job as a crane operator, also discussed firearms laws.
He wrote "mass shootings are new phenomena that cannot be directly blamed on guns".
"Plus there are a lot more guns in Europe and the UK than people think," he added.
Elsewhere on the site, posting in a group for virgins, he complained about being a "virgin" and stated: "I can't attract women at all".
YouTube and Facebook have confirmed accounts belonging to Davison have been removed for violating their policies.
Babcock International, a security and defence engineering company with sites in Plymouth, confirmed Davison had worked as an apprentice since August 2020.
Chief executive David Lockwood said he was "shocked and deeply saddened by the events".
Prime Minister Boris Johnson tweeted: "My thoughts are with the friends and family of those who lost their lives and with all those affected by the tragic incident in Plymouth last night.
"I thank the emergency services for their response."
Plymouth Sutton and Devonport MP Luke Pollard added it was "unspeakably awful" and he was "utterly devastated" to learn one of those killed was a child.
Plymouth City Council said flags in the city were flying at half-mast, while Smeaton's Tower on Plymouth Hoe would be lit on Friday night as a mark of respect for the victims.
People were asked to stay inside and follow police advice as the emergency services responded.
Eyewitness Sharron, who lives nearby and did not want to give her full name, said what happened was "horrendous and so sad".
"Firstly, there was shouting, followed by gunshots - three possibly four to begin with," she said.
"This was when the shooter kicked in the door of a house and randomly started shooting. He ran from the house shooting as he ran and proceeded to shoot at a few people in the linear park up from the drive."
She said the "shooter proceeded along Royal Navy Avenue still shooting".
At the scene
Andrea Ormsby, BBC South West
Shock is the word I've heard over and over again from local people.
I've spoken to several who live here and all of them have said: "It could have been me."
One father told me he had his little girl in his car when he saw people in the road he was about to drive down waving their arms at him.
They were saying: "Don't come down here, there's a shooter, get away."
Other people said their phones have been ringing non-stop with people checking they're safe.
It is a quiet community normally, but one parish priest said everything felt particularly quiet today as people reflect on what's happened.
Johnny Mercer, MP for Plymouth Moor View, described Thursday's events as "tragic" and "devastating".
He said: "There were some fairly traumatic aspects to this incident and as a community now need to come together and try and understand it as much as we can."
Defence Secretary Ben Wallace said he had spoken to Home Secretary Priti Patel and was assured the situation was "in hand".
"I think it a very sad and tragic event and my thoughts are with the families who have relatives and friends who have lost their lives."
He added: "We should recognise the brave police officers who went into a situation with an armed man and under their own threat took decisive action."
Leader of Plymouth City Council Nick Kelly said nothing in his "living memory" compared with the shooting.
He said: "Today our city is mourning and my heart goes out to all those who are directly affected by this incident."
The Bishop of Plymouth the Right Reverend Nick McKinnel said the city had been "left with a legacy of grief and trauma, as well as great anxiety" that would "affect people's lives forever".
Mr Pollard said Ford Primary School and St Mark's Church on Cambridge Road were open from 09:00 BST as a "safe place for our community to come together".
On his YouTube account, now taken down, Davison bemoaned his personal appearance, talked about feeling isolated and his struggle to meet women.
At times he launched into tirades using terms coined by misogynistic online groups of "involuntary celibate" men, known as "incels".
This internet sub-culture encourages men to blame dissatisfaction with their looks, romantic relationships and their lives on women, and the men who succeed in having relationships with them.
Davison refers to these men as "Chads" in his video blogs - and comparisons are not just about personality or confidence, some incels believe they are genetically disadvantaged compared to these men.
He uses other phrases linked to the incel community as well - including "the blackpill overdose". The black pill worldview is essentially the belief that if you're unattractive, you don't deserve love and you are destined to fail and become more unhappy every time you pursue it.
Read more here on the the incel community and the involvement of at least two young men in the US with previous mass killings.
Police and crime commissioner for Devon and Cornwall, Alison Hernandez said many in the community "would have witnessed what occurred, right in front of their eyes, where they live".
"Absolutely devastated this morning," she said. "A lot of us are speechless."
The last mass shooting in Britain happened in 2010 when taxi driver Derrick Bird killed 12 people in Cumbria.
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