"The offenders do not differ at all from neo-Nazis and their fire attacks," Gabriel said in an opinion piece in the Bild am Sonntag. He described the three nights of protests as an "orgy of brutality."
Gabrie labeled the offenders as so-called "autonomists," arsonists and violators.
"Germany's image in the international view is seriously affected by the events in Hamburg" and the "alleged political motives" were a cover for violence. "We now need a fast pan-European search for the criminals, but it may still be difficult to identify them," said Gabriel.
About 100,000 anti-capitalists protested and most were peaceful over thee days before, during and after the G20 summit of government leaders worldwide. But others looted shops and set vehicles ablaze in parts of the city, the second largest in Germany behind Berlin.
On Sunday, Hamburg police said that 186 people were arrested and another 225 detained since summit-related activities began June 22.
More than 15,000 police were deployed to monitor the protests. The police said 476 of its officers were injured.
Police responded with tear gas and water cannons.
Authorities implemented a "Red-Zone" -- an area only for the G20 leaders, their convoys and administrators.
"For Hamburg, the G20 is a wonderful idea but for the real people living here, it's a hard thing -- there's traffic and it's impossible to get around," 77-year-old Hamburg resident Karsten Alpers said to CNN. "These people won't damage anything -- they are peaceful. We are not scared."