The minister's comments came as he announced a drive to prevent white working class people being "exploited" by extremists.
But he later backtracked by stressing that today's situation was "nothing like the 1930s". He said:"All we are facing at the moment is small.
"But I think we need to take it seriously enough to say that there are obviously people who would like to be provocative, hope that there is not just a reaction but there is an overreaction, then people blame the people who overreact and the situation gets out of control."
Mr Denham singled out protests being organised by the English Defence League, some of which have turned violent over recent months.
Except perhaps it wasn't that the English Defence League wanted an overreaction, but that any expression of displeasure with Islamofascists in Britain faces an organized overreaction: Violent race riot flared after mosque chief urged Muslims to confront right-wing 'English Defence League' protesters.
The most influential Muslim leader in the West Midlands urged his followers to 'vent their feelings' against Right-wing protesters during a Birmingham rally that ended in violent clashes and 90 arrests.
Birmingham Central Mosque chairman Dr Mohammad Naseem encouraged Muslims to counter-demonstrate during Saturday's anti-Islamic protest by the English Defence League (EDL).
The police had advised community leaders to stop people from attending, reported The Times.
Last month there were also clashes when the English Defence League - formed after British soldiers were abused by Islamic radicals at a homecoming parade in Luton - held a rally on the same day as the Unite Against Fascism group.
The latest disorder involved around 200 people and spilled on to Bennetts Hill, a street popular with shoppers and lined with a number of pubs.
English Defence League marchers were involved in running disturbances which lasted all afternoon before the Right-wing protesters were taken to another part of the city by bus.
Witnesses claimed the English Defence League marchers, many of whom had been drinking since the morning, ripped up seats on the journey away from the city centre.
But some members slipped away from the police, clashing with more than 30 socialist protesters amid cries of 'Racist scum, out of Brum'. After an hour of angry skirmishes in the city centre, the situation deteriorated further after a group of Asian men also joined in.
Sarah Edwards had to duck into a cafe to avoid being caught in the violence.
She said: 'We suddenly saw what seemed to be about 200 Asian men running down the street, throwing bricks.
'They had bandanas over their faces and were shouting and screaming. We were so scared, we feared for our lives and had to run into the cafe so we wouldn't get hurt. It is so shocking to see this on our streets'
The English Defence League has claimed it is not racist, even saying it did not want any violence to happen at the pre-planned protest.
This picture is a bit inconsistent with the accusation of neo-Fascist skinhead racism: the haircuts look right, but what's up with that flag?
English Defence League supporters hold aloft the flag of Israel and gesture to police as they are corralled into a subway following the demonstration
However, it seems that there really are Islamofascists, known terror suspects, roaming free in the UK. In fact, some of them are even living on the public dole, courtesy of the British taxpayer: Suspects named on United Nations terror list living free in Britain.
The revelation that the men are being allowed to live in Britain without the prospect of being arrested or deported has prompted calls for an urgent change in the law.
Among the 12 suspects named on the UN list are a number of men accused of raising funds for a violent jihadist group with alleged links to Osama bin Laden....
One of the men named on the UN Consolidated List is Mohammed al Ghabra, a 29-year-old British citizen suspected of being a key figure in the plot to blow up passenger airliners over the Atlantic.
Also on the list is Khalid Abd Al-Rahman Hamd Al-Fawaz, 44, a Kuwaiti living in London, who has been accused by the FBI of involvement in bombing American embassies, and Hani al Sayyid al Sebai, a 46-year-old Egyptian also living in London.
Other individuals on the UN list include Ghuma Abd'rabbah, 52, a Libyan-born British citizen who is suspected of raising funds for the Libyan Islamic Fighting Group (LIFG), a jihadist organisation opposed to the Gadaffi regime, and accused of having links with al Qaeda. He is understood to be living in the Birmingham area, along with Libyan-born Abd Al-Rahman Al Faqih, 50, who is also on the UN list....
Individuals are placed on the list on the basis of evidence about their links with al Qaeda or the Taliban submitted by members states of the United Nations. Once their inclusion has been endorsed by the UN Security Council, banking and treasury officials in the individual's country of residence are instructed to freeze their financial assets.
David Davies, Conservative MP for Monmouth and a member of the Home Affairs Select Committee, said: "It's quite outrageous for these people to carry on living here, many of them on benefits. The Home Secretary should have the right to either lock them up or throw them out of the country, but for that to happen requires a change in the Human Rights Act."
A spokesman for the Home Office said: "These individuals are here legally. If they breach any laws they will be prosecuted. We cannot comment on any security operations regarding individuals."
One would think that if the Communities Secretary really wants to damp down fear and resentment toward Islamic extremism in Britain, a good place to start would be to arrest or expel the most extreme of the Islamic extremists.