Paris Mayor Bertrand Delanoe called for Interior Minister Manuel Valls to respond to Tuesday's violence, which stemmed from a victory parade taking place around the Arc de Triomphe.
"The day after the riots that sabotaged this great celebration of PSG's coronation, damaged Paris and deeply hurt Parisians, I would like to express my disgust and anger with regards to the surge of violence that several hundred thugs were responsible for," Delanoe said.
Valls responded by calling a meeting with representatives from Paris Saint-Germain, the French football league, and law enforcement officials, while defending police actions.
Paris Saint-Germain has a "serious problems with its fans," Valls told Europe 1 Radio. "Football is still sick - that's the case with PSG."
Some 10,000 fans waited for more than an hour in the Place du Trocadero, near the Eiffel Tower, and clashes broke out within five minutes of the team appearing on the podium. Riot police fired tear gas and smoke bombs after people threw things and the crowd surged toward the podium.
More than 30 people were injured, including police, and nearly 40 arrests were made, Valls said.
"We must be merciless with these individuals who indulge in violence," against those who present an "intolerable image of Paris and France," Valls said.
Paris police commissioner Bernard Boucault said there would be "no more events like this in a public place for Saint-Germain."
The club released a statement Tuesday:
The party was spoiled by a few hundred troublemakers who have nothing to do with football and even less with those that fill the Parc des Princes on match days with such passion and enthusiasm and in total security.
All the members of the club, the players and the directors, express to all those loyal and passionate fans their heartfelt regret that today's trophy presentation ceremony had to be cut short.
The celebrations will continue this Saturday at the Parc des Princes for the Ligue 1 match against Brest, when the club and its fans will unite in the joy of Paris Saint-Germain's first league title in 19 years.
Paris Saint-Germain is more determined than ever to build a huge European club, worthy of the French capital, and far removed from those intent on trying to destroy that dream.