Both were charged for allegedly creating a rift and spreading disharmony between the Maratha and Dalit communities, he said.
Additional Commissioner of Police (South/North) Ravindra Sengaonkar said their speeches are being analysed and they will be summoned for questioning.
Mevani, the newly elected MLA in Gujarat, and Khalid had attended the "Elgar Parishad", an event organised to commemorate the 200th anniversary of the battle of Bhima- Koregaon, at Shaniwar Wada in the city on December 31.
Bikkad approached the Deccan-Gymkhana police with the complaint, which was forwarded to the Vishrambaug police station, since Shaniwarwada falls under its jurisdiction.
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The Vishrambaug police registered the FIR against the two leaders yesterday, the official said.
According to the complaint, Mevani at the Pune event said, "If we want to win over this new Peshwai, the battle of Bhima Koregaon needs to be taken ahead."
According to the complaint, Khalid, the student leader from JNU in New Delhi, said the battle of Bhima-Koregaon had to be taken ahead.
"They had attacked. It is time to retaliate and we will fight this battle and we will win and this victory over new Peshwai will be the true homage to the martyrs of Bhima- Koregaon battle," the complaint quoted Khalid as saying.
Sengaonkar said, "A police team had recorded the video and audio of the speeches given by Mevani, Khalid and others at the Elgaar Parishad."
"We, too, could have registered the case suo motu (on its own). However, we could not do so since the event got over at 10 pm and thereafter police were busy in December 31st night bandobast.
"But since Bikkad has already filed a complaint and we, too, have all the material, officials of the Vishrambaug police have already started investigating the case and analysing the speeches of both the leaders," he said.
Normal life was crippled in Maharashtra yesterday due to a bandh called by Dalit groups to protest the violence on the anniversary of a battle fought 200 years ago.
Violence erupted in Pune on January 1 when Dalit groups were marking the bicentenary of the Bhima-Koregaon battle in which the British defeated the Peshwas of Maharashtra.