Speaking before a cabinet meeting on Tuesday, Tusk asked ministers to examine all gun laws and the way shooting ranges operate.
He said he wanted to be sure that every firearm in private hands is registered.
He warned, however, against hasty decisions.
"I will not allow anyone in the government to give in to momentary emotion or populist calls," he stressed, noting that some people want unlimited access to guns while others are calling for bans and very strict rules.
Also, Tusk said the state would provide "above-standard" support to all victims of the Kraków shooting and their families.
He praised the fundraising efforts that have already collected millions of zloty.
Referring to the attack, he said the government would return to proposals aimed at what he called the "blatant abuse of freedom" online.
"What is banned and illegal in the real world must also be banned and eliminated online," the prime minister stressed, adding that this was not about censorship but about protecting children and young people.
He thanked those who had refrained from politicising the attack.
He criticised people who had been quick to speculate about the assailant's nationality, language or skin colour, noting that the swift work of police and prosecutors meant more facts were now emerging.
Separately, Tusk said the government would soon adopt a regulation releasing more than PLN 6 billion (EUR 1.37 billion) to police, the fire service, the Border Guard and other agencies.
The money will come from the EU's Security Action for Europe (SAFE) programme, which offers low-interest loans for defence spending.
It had been blocked after President Karol Nawrocki vetoed the law implementing the scheme in March.
Saturday's attack
On Saturday, a 24-year-old man drove a car onto Kraków’s Main Market Square and opened fire with an automatic weapon on passers-by.
Six people were killed and 16 were injured, including two police officers and the attacker, who later died in hospital.
He is also believed to have killed his parents and sister, whose bodies were found in the family's flat in Ostrowiec Świętokrzyski.
(ał)
Source: PAP