A bus was also set on fire in the latest flare-up in the city, where a curfew was imposed yesterday after the clashes.
A state government spokesperson said prohibitory orders still remain in effect in the city in western Uttar Pradesh, but did not specify whether the curfew had been lifted.
A strong posse of RAF and PAC personnel have intensified vigil in the district, whose borders have been sealed to stop elements detrimental to peace from sneaking into the city.
The fresh violence happened a day after a 16-year-old boy was killed and two others were injured in clashes in the city.
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The clashes yesterday happened after stones were reportedly pelted on the motorcycle rally taken out by VHP and ABPV volunteers as part of celebrations on the 69th Republic Day.
The UP police said in a tweet today that they have arrested at least nine people in connection with the violence.
"Our main job at this point of time is to ensure that along with normal law and order situation, brotherhood among communities also remain intact," Kumar told reporters.
He added the police was trying to make people "understand communal bonhomie". "The situation is under control, and will remain so. Sufficient police personnel have been deployed."
Superintendent of Police, Kasganj, Sunil Kumar Singh, said: "Anti-social elements had set two shoe shops afire in Ghantghar market, and fire brigade was pressed into action.
Deputy Chief Minister Keshav Prasad Maurya described the violence as unfortunate, and said the people behind it would not go unpunished.
The state police said today that a complaint has been registered at the Kasganj police station and a special team has been formed to arrest others involved in the violence.
Yesterday, the police said a few unidentified miscreants had hurled stones at the motorcycle rally.