He was speaking as MPs from all the major parties joined in condemning the violence that broke out in the Lancashire town on Saturday and Sunday nights.
Mr Denham said he had launched an inquiry into its cause.
The minister's Commons statement on the disturbances came as police and community groups were holding meetings in an attempt to establish why the trouble took place.
Common elements
Mr Denham also told MPs that Home Secretary David Blunkett was "seeking advice" about any common elements between disturbances in Burnley and those in Oldham in May.
Local MP Peter Pike also repeated his warning that it was "vitally important that people should stay at home tonight and not go out to create more disturbances".
Mr Pike added: "There cannot be any excuse for violence or lawbreaking from any section of the community."
Responding for the Conservatives, David Lidington told MPs: "Nobody should have to feel afraid of walking through any street or district in their own home town."
He asked the minister if the government was looking into the issues of segregated communities and made a plea for the government to boost the resources given to neighbourhood policing.
Recounting the circumstances of the troubles which saw shops and cars burnt out, Mr Denham told the House that "a number of separate spontaneous incidents" sparked the violence.
'Rising tension'
The minister added that a total of 11 people have been arrested as a result of the "deeply disturbing" violence, for a variety of criminal damage and wounding offences.
Following up the minister's remarks that far-right activity was not definitely to blame, Liberal Democrat home affairs spokesman Simon Hughes said it was his experience that: "The more right-wing activity you get the more the tension rises."
He asked if enough was being done to prosecute those using language or writing pamphlets inciting racial hatred.