Ralf Jäger told journalists in Düsseldorf on Monday that the authorities “must convince the courts to forbid such demonstrations in future."
“This was no political demonstration, but a platform for violence,” he added.
Jäger said the hooligans had “misused the freedom of assembly”.
Politicians and police leaders were shocked by the scale of the violence committed by participants in the demonstration, which was purportedly a protest against Islamic extremism.
The gathering drew together members of far-right political parties including the anti-Islamic Pro NRW and Die Rechte with usually-opposing groups of violent football fans.
Jäger, a Social Democratic Party (SPD) politician, had to move quickly to respond to criticism from his Christian Democratic Union (CDU) opponents in the state parliament.
“My impression is that the situation wasn't properly understood,” CDU leader in NRW Armin Laschet said on Monday.
“It was obvious that far-right supporters would come to Cologne in large numbers.”
GALLERY: Police battle thugs in Cologne
One anti-Muslim blog called Sunday's violence “the miracle of Cologne”, claiming it “resembled the first demonstrations which helped bring down the unjust system of the GDR [former East Germany].
“Against Salafists, nice words are of very little use, but physical presence sends them back to their hiding-places," the author wrote.
Meanwhile, mainstream football fans' organization Pro Fans sought to distance itself from the image of the hooligans who took part in the weekend's violence.
“What's new about this is that it no longer has anything to do with football,” spokesman Sig Zelt told the Westdeutsche Allgemeine Zeitung.
“We as Pro Fans denounce what they're doing.”
Federal Justice Minister Heiko Maas, added that “those who bring violence into German cities must be pursued and punished with all the powers of the rule of law".