You need to keep in your mind few things while applying visa of Russia outside from your home country.
First we strongly recommend you to call your nearest Russian consulate or embassy in your current location. They will ask your visa status in that current country and then tell you in detail that you can apply or you need to go back to your homeland to apply Russian visa.
Second, as per our knowledge you cannot apply Russian visa outside your country if you are having tourist or any temporary visa status. But, resident visa holders may apply outside of their home country.