bapu well that is interesting. All I can say is things must be loud where you are then. What I have found works well in some situations is using a downward expander setup on the mic signal on the way in preferably. You can set it in such a way as it will drop the gain right down between words and as soon as you make any sound it opens up again. If you are careful about it you can also set the release carefully (faster) and it can end up virtually transparent.
What that will do is kill any background room tone and outside noises. Yes the unwanted stuff will still be there when you sing but the signal should mask the noise very well. You are only really noticing the stuff in between your words.
Another option is to record as you do and try setting that up over the vocal track after the event.
(in post) Sometimes I have to do this when I am recording relaxation voice overs for clients. They speak really soft in that situation and I have to take measures to quieten down the room tone.
(and my space is real quiet!) It usually works well because there is often music under the final thing too and you dont hear it.
Be careful sampling the room tone and trying to remove it using noise reduction. You can get into more trouble sometimes doing that. (vocals can get skewed up)