They have still not been able to establish a clear motive, they said.
On February 4th, 35-year-old Rickard Andersson entered the Campus Risbergska adult education centre in the city of Örebro and shot dead 10 people before turning his gun on himself.
Deputy commander Emelie Bodegrim told journalists they had a "fairly clear picture" of the day in question, but they were investigating a three-hour gap to establish what Andersson did before he was seen at the education centre at 11.30am.
Police said they knew he had taken a bus to a street close to the school that morning, arriving at 7.47am.
Police published a photo showing Andersson the morning of the attack, dressed in dark clothes and carrying a guitar case and a blue Ikea-bag. They asked members of the public to get in touch if they had any information.
They also provided more details on the timeline of the shooting, saying officers had arrived six minutes after receiving reports of the shooting.
The first police patrol entered the school at 12.40pm, one minute after arriving, and within minutes the gunman had opened fire on them.
But officers could not immediately safely return fire, said Bodegrim.
"From the time the perpetrator opened fire on our patrol, only two shots were fired, one shotgun blast that did not hit anyone, and another shot that ended the perpetrator's life," Niclas Hallgren, deputy regional police chief, told reporters.
Police said the victims had apparently been targeted at "random" and that they had recovered 70 empty shell casings from the scene.
Bodegrim said they were still looking into establishing a motive, and were looking into the perpetrator's living situation, but warned that they might never know. They have already described him as an unemployed recluse.
Police say he had no prior criminal record and a hunting licence for four guns.
Police have not publicly named the victims but the foreign backgrounds of the majority of them soon came to light when their names and photos were published in Swedish newspapers and on social media, sparking concern among the country's immigrants.
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