I would suggest starting to plan the move out. If the landlord is so dismissive of a potentially life-threatening hazard, makes you wonder what else can they be lax about.
There may be a number of issues there, including issues with the apartment wiring as well as the internal wiring of the appliance. There may be a cord that the appliance could be standing on that will get "chewed" through the insulation with time. There can be an number of things gone wrong, any one of which requires immediate electrician's attention.
I would suggest that you stop using the stove and call the electrician yourself, immediately, then present the invoice to the landlord for payment. It's your life on the line after all. Good luck with resolving the situation.