hi i need some advice.

I tendered my resignation with a month notice as required in my contract. BUT my GM wasn't happy with it as he says it was too short notice for him to get an replacement. He wanted me to work till he find a replacement or at least give him 2 month notice on good relation basis.
I wish i could stay for another 2 months but my new employer would not be able to wait that long.

Should i give another 2 weeks, total 1.5mth as good will? Coz my contract is clearly stated 1 month notice period.