You'll have to weigh-in the benefits and the demerits of joining both companies.
The easiest thing to do would be to stay at the company you're expected to join next week. It would also cause no problems with the company. It's also the most ethical thing to do. Especially since you don't have the letter of offer for the other company yet.
I don't want to lose the new job that I have to join next week in a assumption that everything will go smoothly for going to other company outside.
It's a hard choice, obviously. You have to pick between something you know will reward you or gamble with a job that you really want but has many risks(No letter of offer yet, getting a work visa, moving out of India, backlash of burning bridges with other company ,etc.)
I really don't want to tell them that I am trying for another company and that's the reason I want you to extend my joining date
After reading up a bit on India's 3 month notice period in the IT sector, I can understand why you would want to extend your joining period. Ask for an extension on the join date. Tell them that you have personal things to attend to and if they pry too much just tell them you're not comfortable saying much more.
If you do get the letter of offer, it'll be up to you to find a way to tell them you'll be working abroad instead of joining them but at least there shouldn't be any legal issues. I still find it sort of unethical but you have to remind yourself that you're your own person and you should do what makes you happiest.
If you don't end up getting the letter of offer during that extension, you still have options: If after you've joined the company and the abroad company sends you the letter of offer, ask them if they would be alright with waiting for 3 months. You could explain to them that it is part of your contract(correct me if I'm wrong here) to give a 3 months notice but it would also help you get a work visa and find a place to live.
You would be burning bridges but if you think the results outweigh all the issues you'll have to face, go for it. I don't think it's that uncommon for people to leave early for better opportunities.
Hope this helps a bit.