KOLKATA, India — Police in India fired tear gas and water cannon to disperse hundreds of protesters marching in the eastern city of Kolkata on Tuesday to demand the resignation of a top state minister in the wake of the gruesome rape and murder of a trainee doctor.

Protesters led by university students broke through the iron barricades set up on the route of their march to the West Bengal state secretariat, television footage showed, resulting in a baton charge by the police, who had…