Home Secretary Jacqui Smith said on Wednesday police officers could face criminal probes if an inquiry into events that culminated in the death of a man during G20 demonstrations in London showed action was warranted.
Ian Tomlinson, 47, a newspaper seller, collapsed and died from a heart attack soon after the incident in a street by the Bank of England, shown in footage on the Guardian website.
The Liberal Democrats said the incident in the video was "sickening" and have called for a full criminal investigation.
The Conservatives also said it was right that there should be an independent inquiry quickly.
London's police chief admitted the video images raised concerns and Smith agreed there should be action if that was the conclusion of an Independent Police Complaints Commission (IPCC) inquiry.
"I'm glad that the IPCC themselves called for further evidence in order to do that investigation as quickly and thoroughly as possible," she told the BBC.
"If it identifies the need for a criminal investigation, that also needs to be pursued."
The video, filmed by a New York fund manager who was in London on business, shows Tomlinson walking alone with his hands in his pockets in front of a line of police officers, some with dogs and others equipped with riot helmets, shields and batons.
One officer appears to lunge at Tomlinson from behind, pushing him with enough force to send him sprawling on the ground. Tomlinson is then shown sitting up and apparently remonstrating with the officers, before bystanders help him up.
He is then seen walking away past a line of dog handlers.
Minutes later he collapsed in a nearby road, Cornhill.
Police attempted to resuscitate him before he was taken by ambulance to hospital where he was pronounced dead.
"Ian clearly had his arms in his pockets and back towards the police. There is no need for them to step in towards him," Tomlinson's son Paul King was quoted by newspapers as saying.
"(The video) clearly shows that Ian did have an altercation. Now we can say, 'yes he did.' Up until now it has been 'if'. But now we've seen it, we want answers."
The IPCC said it was analysing the video and other evidence.
Witnesses had told the police watchdog that Tomlinson did have contact with officers before he died, but until now this had not been shown in photos and CCTV pictures obtained of the man making his way home through the protests.
"This video clearly shows an unprovoked attack by a police officer on a passer-by," said the Lib Dems' justice spokesman David Howarth.
"The officer concerned and the other officers shown in the video must immediately come forward."
Conservative shadow home secretary Chris Grayling said: "these latest revelations are extremely alarming and leave big questions to be answered by the police."
Human rights group Liberty called for policing at public protests to be closely scrutinised.
"Clear images of an armoured policeman assaulting an innocent bystander from behind impugn the whole attitude to policing protests by the Metropolitan Police," said Liberty's Shami Chakrabarti.
"The IPCC failed its first major test in the (Jean Charles de) Menezes case. If the Commission is to regain a shred of public confidence, it must do far better in terms of speed, sanction and transparency," she added.