Mevani 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.
According to the complainants -- Akshay Bikkad and Anand Dhond -- Mevani and Khalid had made "provocative" comments at the event.
Bikkad and Dhond, both locals, approached the Deccan Gymkhana police station with an application and demanded the registration of a case against Mevani and Khalid for allegedly promoting enmity between different communities.
"Mevani provoked the people to come out on the streets and retaliate. Due to this statement, people took to the streets and tension gripped the city," according to the complaint.
A senior officer attached to the Deccan Gymkhana police station confirmed the receipt of the complaint application.
Clashes between Dalit groups and supporters of right-wing Hindutva organisations during the 200th anniversary celebrations of the Bhima-Koregaon battle in Pune district had left a man dead yesterday.
The clashes broke out at Bhima-Koregaon when people were headed towards the war memorial in the village, about 30 km from Pune city, the police had said.
Dalit groups were celebrating the bicentenary of the Bhima-Koregaon battle, which the forces of the British East India Company had won over those of the Peshwa.
Dalit leaders commemorate the British victory as it is believed that soldiers from the Mahar community -- then considered untouchables -- were part of the East India Company's forces. The Peshwas were Brahmins and the victory was seen as a symbol of assertiveness by Dalits.