The following pointers are based on personal experience. They may or may not apply to your specific case.
What not to do:
For starters, how about not pulling over? That's a big no-no. Even if those lights are inside the car and not on top, it is a safe bet to assume that it is actually a police car, and not just someone who likes psychedelic lights inside his vehicle. Understand that the average American has a different concept of driving ambience than an Indian auto-rickshaw driver.
Once you realize it is indeed a cop car that is chasing you, it is advisable not to continue driving while you try and come up with an excuse for why you were speeding. It is best if you pull over right away, and manufacture your plea while the cop is running your license plate number through his computer. If the cop car has to overtake you and force you off the road, all bets are off and it would be safe to assume that any excuse you now offer will encounter a cold reception regardless of it's credibility.
Once you are forced off the road by the cop and have parked your vehicle behind his, if he asks you to get out of your car, make sure you engage the hand brake first. If your car lurches ahead the moment you disembark, and crashes into his car, that might cause some distress to the officer and further harm any possibility of friendly discourse.
Now that you have had a lot of time to think up an alibi, it is now up to you to convince the cop of your innocence. But, if after spending all that available time, the best you could come up with was that it was necessary for you to speed in order not to miss the green light at the intersection, it reflects badly on you and your resourcefulness. While you are trying to sell your version of the story to the cop, if your friend in the back seat gives you a look that says "Stop talking. Stop talking now.", it means that your excuse is not finding a sympathetic audience with the officer and it is now time to cut your losses and withdraw. There will always be the court appearance where you can defend yourself with more preparation under your belt.
What to do :
Always keep your Indian license with you (if you have one), preferably, in tatters. This could help you in some rural parts of the country where the cop, out of sheer ignorance of the etiquette in such matters, will prefer to let you go instead of dabbling in vague and shadowy sections of the law dealing with foreign licenses.
The second method one can use is called the "Puzzled Foreigner Approach".
I was in Milwaukee on a business trip, and after having dumped all my stuff in my motel room, I took off in my rental car to explore the city. I was driving along the northern lakeshore suburbs, admiring the residences of the city bourgeoise. Since it was a residential area the speed limit probably was 35 or so. I had my eye off the road and so apparently I started to speed up a bit and suddenly, saw flashing lights behind me. "Goddamnit", I thought, "What is it about rental cars that attracts cops?" The officer pulled up behind me, walked over to my window and God Almighty, it was a female. After completing the license and registration formalities, she asked me why I had been speeding in a residential neighbourhood. I dont know whether it was the realization of my life-long dream to be pulled over by a female cop, but my brain suddenly went into overdrive. I saw the reams of maps my company assistant had printed for me, and my face automatically turned on the glassy-eyed confused stare. I started babbling about how I was not from this city, and that I was looking for my motel (which was on the other side of the city actually), even showing her the maps lying on the front seat as proof. I also told her I had been following this road for the past half an hour (which was actually the truth), and that the road just kept going on and on and on. She must have been convinced by my incoherent rambling story, because after giving me full directions to my motel, she let me go without so much as a warning.
(disclaimer : This method has not been tested on male cops)