I (and a lot of Europeans) use a man's handbag. Saves stuffing yr pockets with keys, wallets, phones,notepads, pens, mascara (only joking there). I assume that "purse" is the American for handbag, so that would be a purse for men.
Don't know if they sell them in the states, but I got mine from a department store in Barcelona. Lots of different sizes and manly designs.