Sports Minister Gerry Sutcliffe has described the violent scenes at last night's West Ham versus Millwall Carling Cup match as "a disgrace to football".
Sutcliffe also backed the Football Association's call for life bans for those found to have been involved in the incidents inside and outside of West Ham's Upton Park stadium.
The FA are examining the events that saw a man stabbed outside Upton Park and pitch invasions occur following West Ham's goals. West Ham have pledged to help with the investigation but could also face action themselves.
A spokeswoman for the Metropolitan Police confirmed officers made several arrests and were scanning CCTV footage to identify hooligans.
Sutcliffe said: "The scenes last night were a disgrace to football.
"I completely back the FA's call for any person identified as involved in the violence to be banned for life and urge full and swift co-operation from all parties in the investigation into what happened.
"We have made great progress in the past 20 years in tackling football hooliganism in this country and we will not tolerate any return to the dark days of the 70s and 80s when it plagued the game.
"We will never be complacent in the fight against football violence."
Both the Football League - whose competition the Carling Cup is - and the FA have condemned the violence.
FA director of communications Adrian Bevington said on BBC Radio Five Live: "We have to understand exactly what measures were put in place last night.
"I'm not going to condemn West Ham or Millwall football clubs for any of their actions - certainly not at this stage, because we don't know exactly what's been put in place.
"And we know there have been huge efforts on the parts of all our clubs to try to eradicate the problems and we've had a history of success on that.
"However, we have to make sure that the individuals concerned face such tough actions that they can't go to football again."
Football League chief operating officer Andy Williamson said: "We utterly deplore the violence that took place at last night's match between West Ham United and Millwall.
"Such behaviour has no place in the game and we will work with all the relevant authorities to ensure that those behind it are held to account.
"Football has made huge progress in the last 30 years in the management of football matches and the whole game must continue to demonstrate that such behaviour will not be tolerated."
Football Supporters Federation chairman Malcolm Clarke, due to meet with FA chief executive Ian Watmore today, recognised the "very serious" nature of the crowd disturbances but stressed that "hysterical over-reactions" would not be helpful.
Clarke added: "I can assure you the vast majority of Millwall and West Ham supporters will be as horrified by events that occurred as everybody else."
He explained: "I have a routine meeting with the FA chief executive today - I'm quite sure this will now be on the agenda.
"There clearly needs to be a very clear response to try to make sure this doesn't happen again."
Clarke is aware that football still has a hooliganism problem, even if such large-scale incidents are rare.
"We haven't eliminated it, that's certainly true," he said.
"We haven't yet had figures for last season but Home Office figures for the four previous seasons to that showed the lowest level of disorder since those records started being kept."
He added: "Anybody who goes regularly to football matches and has done for 20 or 30 years as I have, is in no doubt that the amount of disorder is far less than it was, say, 20 years ago.
"That is not to diminish last night, that was obviously an extremely serious matter.
"The question is, why did it occur at that particular game when the trend over recent years has been in the opposite direction?"
Clarke urged those who look at last night's disturbances to examine whether the authorities were prepared for all possibilities.
"Part of the investigation would need to look at whether appropriate measures were put into place to deal with the situation," he said.