The cost of policing similar protests in Manchester was about £200,000
Young Muslims have been urged to stay away from parts of Leeds on Saturday as the English Defence League (EDL) stages a protest against Islamic extremism.
Thousands of people are expected to attend the EDL's rally in City Square and a rival protest by Unite Against Fascism (UAF) in Victoria Gardens.
Hundreds of police officers will act as a barrier between the rival protesters.
Police visited mosques in the city on Thursday to urge young people not to get drawn into any disorder.
Dozens of people were arrested when trouble broke out at similar protests in Manchester earlier this month and in Birmingham in September.
Don't get drawn in, let the police handle the event, let people stage their protest then go on their way
Ch Supt Mark Milsom
Ch Supt Mark Milsom, from West Yorkshire Police, said: "We have been involved in ongoing discussions with both groups about their respective events, our aim being to facilitate peaceful protests, with minimum disruption to the public.
"We expect there may be some disorder, given previous events elsewhere and have plans in place to deal with that."
Mr Milson said because of the EDL focus on Islamic issues, members of local Muslim communities, particularly younger people, "might feel threatened and be tempted into attending".
Arshad Chaudhry, of the Leeds Muslim Forum, speaks about his concerns
He said: "This would potentially play into the hands of both groups and I want to reinforce the message we have been taking to those communities.
"Don't get drawn in, let the police handle the event, let people stage their protest then go on their way."
Mr Milsom said the protests were away from the city's main shopping areas and people coming in to Leeds to shop would be unaffected.
He said the majority of people at the demonstrations wanted them to be peaceful, but anyone who did become involved in disorder would be arrested.
He added: "Whether or not people agree or disagree with the points of view, there is that right to freedom of speech.
"Clearly it has to be peaceful and we are looking to ensure that."
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