He also asked those who sought to combat fascism "to hold their hand carefully, to allow us to deal with public order and not to take it in any way into their own hands".
Trouble flared in the predominantly white areas of Bierley and Fagley, where youths armed with missiles attacked property.
Despite the arrests, West Yorkshire Police said the violence was "minor and sporadic" compared with previous days and there was no serious disorder on the streets.
Chief Superintendent David Collins said most of the trouble was caused by young people and urged parents to keep an eye on their children and ensure they were not involved.
Earlier on Tuesday the home secretary said the "wanton destruction and violence" of the Bradford riots would not be tolerated.
David Blunkett condemned the behaviour of the rioters, telling the Commons he would not put up with it.
He added that tackling the social ills behind the disturbances must happen after order was restored.
Ministers are already examining what can be done to prevent the violence recurring.
An "inter-departmental ministerial group" looking at the wider problems will publish preliminary details of its findings shortly, said Mr Blunkett.
'Fascists and Nazis'
And projects running in the area over the summer will attempt to bring together young people from different religious and ethnic backgrounds.
The home secretary added that organised thugs from whatever background undermine the possibility of creating an inclusive society and "the threat from them must be met head on".
"From today we will not accept the destruction of hard won improvements in the most difficult areas of our country," he said.
"Whatever the debate about alienation and disaffection - attacking the police, destroying the well-being of the local community and playing into the hands of organised groups will simply not be tolerated."
Mr Blunkett said that had the National Front not sought a march and demonstration in Bradford "peace and quietude" would have continued.
He also asked those who sought to combat fascism "to hold their hand carefully, to allow us to deal with public order and not to take it in any way into their own hands".
Terry Rooney, MP for Bradford North pointed to the role of the far right in other recent riots.
"These organisations [NF and BNP] are purely out to foment racial hatred. There is no place on the streets for these fascists and Nazis."
He said the time was coming when Parliament must consider proscribing these organisations.
Liberal Democrat home affair spokesman Simon Hughes suggested public order legislation be looked at with a view to making it less possible for people to exercise their "rights" when all they were seeking was to provoke tension and racism in urban communities.
For the Opposition, David Lidington called on the home secretary to launch an "urgent inquiry into policing pressures in Bradford and elsewhere in West Yorkshire".
Mr Lidington said there was concern in Bradford that the police were too stretched.