Kasyanov denounced Sunday's riot opposite the Kremlin in downtown Moscow as a result of "pre-meditated attacks by vandalising hooligans, not real supporters," who set fire to cars and smashed shop and restaurant windows.
"If such an event is repeated, the police and city authorities should ask themselves if Russia still has a right to vie to host the European football championship in 2008," Kasyanov added.
Russia's deputy sports minister Nikolai Parkhomenko described the troublemakers among 8,000 people who watched Sunday's match on a giant screen in Manezh square as "animals."
"This is the worst possible publicity for our country that you can imagine. Without doubt, it will not help Russia's chances of winning the right to hold the European championship finals," he said.
World football's governing body FIFA said it "regretted" the Moscow riot but recalled similar trouble occurred in Russia during the 1994 World Cup held in the United States, and blamed excessive alcohol consumption and inadequate policing.
"There was rather a large amount of alcohol. What happened had nothing to do with real football fans. FIFA distances itself totally from what happened," FIFA spokesman Keith Cooper said.
Moscow police chief General Vladimir Pronin tendered his resignation Monday but Interior Minister Boris Gryzlov told Interfax he had rejected the general's offer to step down.
One policeman wounded in Sunday's alcohol-fuelled riot opposite the Kremlin died in a Moscow hospital early Monday, the Interfax news agency reported, although the interior ministry denied to AFP that there had been any fatalities.
Eighteen police officers were injured in the rioting, which broke out after some people watching the match went on the rampage when Japan scored the winning goal, a police spokesman told AFP.
One man was stabbed and died in a car on his way to hospital, the Russian prosecutor-general's office said.
Police said 113 people had been detained on suspicion of fomenting the riots, while the chief police investigator said a link to possible extremist infiltration had not been ruled out.
However senior investigator Vitaly Mozyakov said police did "not yet have hard information about the fact that the mass rioting was deliberately prepared beforehand, and was a planned action."
"As a result, it's too early to talk about extremism," Mozyuakov told RIA Novosti news agency.
Around 35 people civilians were hurt in the post-match disturbances and nine were taken to hospital, though none were in critical condition, the interior ministry said.
Five Japanese musicians attending the city's 12th Tchaikovsky festival were among those injured in the rioting as irate fans vented their anger at Russia's dismal World Cup performance.
Prosecutor General Vladimir Ustinov spoke of the country's shame at witnessing the drunken rampage that caused the civilian's death, but appealed to Japan in particular not to interpret the widespread violence as racist.
"We think that the outbreak of hooliganism was not in any way a sign of disrepect for the state of Japan or for Japanese people living in Russia," Ustinov told a joint press conference with US Attorney General John Ashcroft.
Fans set fire to cars parked near Manezh Square, smashed the windows of shops and restaurants on Moscow's main thoroughfare, Tverskoi Boulevard, and rushed the State Duma or lower house of parliament, attacking policemen.
They also attacked an ambulance, breaking all its windows and severely beating up its driver and a field nurse.
Flares of violence continued well into the night as a group of skinheads attacked a Vietnamese dormitory late Sunday, smashing windows and glass doors, police said.
Russia's football association chief Alexander Tukmanov condemned the fans, who he said "behaved like wild beasts," and called on the police to "quickly cut short this hooliganism."
Police reported the situation in central Moscow under full control some two hours after the match ended, but immediately beefed up security at embassies and foreign missions.