Notice period recovery

I joined a firm based on their offer letter. After joining, they never provided me an employee agreement to sign. After two weeks of joining, I decided to resign and leave. I returned all company assets. I had not been trained during my stay. After few days of resignation, the company sends me a notice saying that I'm in violation of the employee agreement which obligates me to serve 2 months notice as I was a confirmed employee. So now I need to pay up the entire salary of those two months (including the variable pay). There is also a threat that if I don't pay, strict action and consequences will follow at my own cost. They also reserve rights to take legal action. The fact is that I didn't sign any employee agreement. I had no idea about any of their employment conditions. The offer letter doesn't mention anything about the notice period. Had I known about it, I would have discussed and probably taken a leave or served the entire period. Now, does the company have a reason to sue me? Do I need to respond to their notice? The threatening language used in their very first notice is worrying! This looks like extortion to me.