They say it is too early to establish what drove the 24-year-old gunman.
The attacker, named as Michał Oksiński, drove a car onto the city’s Main Square on Saturday and "opened fire on random people," officials said.
Sixteen people were injured, including two police officers and the gunman himself, who died in hospital early on Monday.
No charges were filed because of his death, prosecutors said.
Police also found the bodies of three of his relatives, his parents and sister, at the family’s flat in Ostrowiec Świętokrzyski.
Prosecutors say everything points to the same man having killed them earlier.
Each had been shot twice in the head area and appeared to have been killed at night.
An expert has said preliminarily that they died on Saturday morning or overnight from Friday to Saturday, but exact times will only be known after post-mortem examinations.
Prosecution spokesman Przemysław Nowak said investigators found four firearms in the attacker’s car, two AR-15 rifles and two pistols, along with about 500 additional rounds of ammunition.
Between several dozen and possibly several hundred shots were fired in Kraków, he said.
The gunman had held a firearms licence since March for one rifle and one pistol, and had trained at a shooting range.
Nowak said early information suggests he practised only static shooting.
Investigators are examining his motive, any possible inspiration and whether anyone helped him.
Nowak repeatedly stressed it was too early to speak of the reasons behind the attack or any ideology.
A yellow Gadsden flag, a historical American symbol showing a rattlesnake, hung in the gunman’s room.
Nowak said it carries various meanings, including rebellion against authority, and that no obvious far-right or far-left symbols were found in the flat.
Of those injured, two have left hospital and seven are in a stable condition, he added.
The others are seriously hurt, two of them critically.
The two wounded police officers have regained consciousness.
(ał)
Source: PAP