Katainen was reacting to an incident in which three young men became violent when they were refused admission to a discussion event on a book probing Finland's extreme right, attacking with a knife and bottles.
Writing in his blog on Thursday, the PM said there should be zero tolerance for violence related to the freedom of speech and assembly. He said the case indicates that the atmosphere in Finland's societal debate has gone terribly wrong.
"Increasingly hard-edged expressions have in a way become acceptable, and sometimes speech that suggests physical acts against others is dismissed with a shrug of the shoulders," he wrote.
Räsänen warns against making assumptions
A security guard was injured in Wednesday's incident, though not seriously. Police are considering charges of aggravated assault.
In October, Katainen himself was confronted by a man with a knife during an election rally in Turku. He was unharmed.
Interior Minister Päivi Räsänen also strongly condemned the Jyväskylä incident on Thursday. She says that authorities are carefully checking the backgrounds of those involved, including any possible links to extremist groups.
Räsänen warned, however, against jumping to conclusions before the investigation is complete.
One of the authors of the book under discussion in Jyväskylä, Dan Koivulaakso, was the victim of a gas attack last summer in Oulu.