David Cameron has warned against knee-jerk changes to gun laws in the wake of the "horrific events" in Cumbria.
The PM, who will visit the county on Friday, expressed sympathy with communities "deeply torn" by Wednesday's shootings which left 12 people dead and 11 injured.
Inquiries continue as to why Derrick Bird went on the rampage amid reports of a possible family row over a will.
The taxi driver, 52, was pursued by armed police before shooting himself.
Eight of the injured are now in a stable or comfortable condition in hospital. The remaining three have been discharged.
Charles Brett, clinical director of emergency care at West Cumberland Hospital, said five people treated there had gunshot wounds to the face.
"It appears [Bird] was firing out of a car window at head height. It's clear he was directing at the face and head," he said.
However, he said he could not speculate as to whether this was Bird's deliberate intention.
Speaking at a press conference, Mr Cameron said: "These clearly are absolutely horrific events, [a] really terrible situation that has taken place in our country, over the last 24 hours."
The prime minister said he would do everything possible to help "mend the hurt" of communities and "to make sure that everything is done to make sure that events like this cannot happen again in our country".
However, he said the UK's rules on firearms ownership were already among the world's toughest.
"We shouldn't make any knee-jerk reaction to think that there is some instant legislative or regulatory answer," he said.
"You can't legislate to stop a switch flicking in someone's head and for this dreadful sort of action to take place," he added.
More than 100 police officers are investigating the killings, following up more than 1,400 calls relating to more than 30 crime scenes across 25 miles of the county.
Cumbria Police recovered a shotgun and .22 rifle with telescopic sight and have since confirmed that Bird was licensed to own both weapons. He is believed to have done so for 20 years.
Deputy Chief Constable Stuart Hyde said: "We are not able to really understand the motivation behind it - or establish whether this was a premeditated or random attack.
Mr Hyde said officers would speak to people "about him, his life, what has gone on in the last few days, what might have turned somebody into a killer".
It has been reported Bird may have been involved in a dispute over a will. Police have confirmed solicitor Kevin Commons is among the dead.
Other reports suggest he had fallen out with fellow taxi drivers in a row about fares.
A friend reported a brief conversation he had with the taxi driver the night before Wednesday's massacre, which ended with Bird warning: "You won't see me again."
The following day Bird is believed to have left his home in the village of Rowrah and begun the carnage by shooting dead his twin brother David, at his home at High Trees Farm, Lamplugh.
He then travelled to Frizington, where the family's solicitor - 60-year-old Mr Commons - was killed on his driveway.
Next, Bird drove seven miles to Whitehaven where he shot dead fellow taxi driver Darren Rewcastle before heading through villages and countryside in west Cumbria, apparently choosing his targets at random.
Retired Sellafield worker Kenneth Fishburn, who was in his 60s, was shot dead in Egremont, while Susan Hughes, also thought to be in her 60s, was killed while carrying her shopping in the town.
The gunman then moved on to the village of Wilton where he killed husband and wife James and Jennifer Jackson.
Part-time mole catcher Isaac Dixon, aged in his 60s, was the next to be targeted - he was shot and killed at the edge of a field in Carleton.
Then, in Gosforth, Bird shot dead rugby league player Garry Purdham at point blank range as he worked in a field.
Mr Purdham played semi-professionally for Workington and Whitehaven, and was the older brother of Harlequins skipper Rob Purdham.
There were further shootings in Seascale, where cyclist Michael Pike, 64, and Jane Robinson, who was in her 70s and delivering Betterware catalogues, were both killed.
Mr Pike's daughter Jude Talbot said the former Liverpool shipbuilder, Sellafield worker and trade union organiser was known by "practically everybody" in the community.
Dr Barrie Walker, a local GP who was called to the scene of the Seascale shootings, said two young girls had witnessed Mr Pike's killing.
He said: "He was shot twice by the perpetrator and these two girls were watching it and he looked straight at them and these kids were mute for the next two hours.
"It's a beautiful area... to see this kind of carnage in the streets. There was blood running in the gutters of the streets of Seascale and this is just something you don't expect."
The final victim, 23-year-old estate agent Jamie Clark, was driving through Seascale when Derrick Bird opened fire at him.
It was unclear whether he died from gunshot wounds or the resulting crash.
His employers - lettings firm Belvoir - have paid tribute to "one of the nicest lads you could ever hope to meet".
Floral tributes have been laid at the scenes of the shootings across the county.
Bird was eventually found dead in woodland in Boot, shortly after crashing his car near the River Esk.
Don Reed was one of the first people he had opened fire on in Whitehaven - but survived with a wound to his back.
Mr Reed, a taxi driver, said he saw Bird's car approach the back of his rank.
"He shouted Darren Rewcastle... and then he just opened up with a single-barrelled shotgun with a telescopic sight on it.
"He then drove up by me and just pointed it at me, and I just took a flying dive and he caught me in the back. I went on the floor and then I crawled along the taxi rank.
"I was going to apply first aid to Darren, but when I saw Darren, he was gone."
As Bird approached, Mr Reed said he crawled away, opening car doors to protect himself from shotgun blasts.
However, when a friend shouted, Bird got back in his vehicle and drove off - shooting another man in the face as he left.
Counselling sessions are being offered at the psychology department of the West Cumberland Hospital for anyone affected by the shootings.