The prohibitory orders would be in force till September 8, a senior police officer told PTI.
"As a preventive measure, we have enforced Section 144 of the CrPC in Delhi in 11 police districts," said SBK Singh, special commissioner of police (Law and Order, North).
The national capital has 13 police districts. North and central districts will not fall under the ambit of the orders, since no incidents were reported from there, the officer said.
In a Tweet, he also assured Delhiites about adequate security arrangements being in place.
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"All SHOs, ACsP, DCsP and Jt CPs are patrolling the area to prevent any kind incident which may arise due to Ram Rahim followers in Delhi (sic)," he posted on Twitter.
Fire department officials said they received calls about fires from Khyala, Badarpur, Manglapuri, near Babu Jagjivan Ram Hospital, Mandoli, Mehrauli, Samaypur Badli, Anand Vihar Railway Stataion and other parts of the city.
Incidents of arson targeting buses were reported from several parts of the city.
Delhi Police Public Relations Officer Madhur Verma said five "miscreants" were arrested for allegedly attempting to set buses ablaze in Badarpur and Khyala areas.
He said cases have been registered and it is suspected that these people are followers of Dera Sacha Sauda Chief. Police have procured CCTV footages for further probe.
Delhi Police officers are on a night vigil, he said.
Police said some people pelted the bus with stones, when it was coming from Bhajanpura, and as the driver and the passengers fled, they set it ablaze.
A fire also engulfed two coaches of the Rewa Express stationed at the Anand Vihar Railway Station here. Railway officials said it was not immediately clear if it was a case of arson and that investigations were underway.
Police said they arrested one persons in connection with an attempt to torch a DTC bus in Badarpur. He also attempted to set ablaze a cluster bus, they said, adding he is suspected to be a sympathiser of Ram Rahim.
In a tweet, Delhi Police Commissioner Amulya Patnaik assured the citizens of police being at their service in this situation.
"Adequate police arrangements in place & Law & Order situation under control. Officers with reserve force on rounds to maintain peace.
"Appeal to all to maintain peace & order. #DelhiPolice on full alert. Strict legal action will be taken against miscreants for any violation (sic)," he posted on Twitter.
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