It is not clear to me if you already have an offer letter: if you have no offer letter you have nothing. Can you confirm that the offer letter is in your hands in writing?

@Paolo , the new HR told me that once i confirm him that i am joining in 45 days , he will send me the offer letter.

Then you have nothing. Do not go to your HR because you have no new job! You have no decision to take until the offer is in your hands. Sorry...

@Paolo how do i convince the new HR to give me 60 days time to join.

Where are you working? The rules about notice periods, and consequences of not following them, vary between countries.

I have added "India" to the tags, in the hope of getting input from people who know about relieving letters etc. in this situation.

Guys, the new Company says that they will give me the offer letter only when i can join in 45 days, so my point is how can i convince the new HR to hire me and extend the time to 60 days, it is just 15 days more than what they want.... Any pitch that i can say to them?

@VishwaRatna They are unreasonable and abusive, why do you think that will change once you work there? This is a huge red flag. Don't hurry. But probably they also told you that offer is only valid for a few days.

@Chris , my big brother also told me the same thing that you told... the thing is that I really wanna switch from service based to product based company...don't know if i will get similar opportunity next time. Thanks for your suggestions

@VishwaRatna maybe it is not clear enough: run away from the new employer, quick, far and fast. If strangers on the net give you the same advice as your big brother please understand that you may be badly wrong. Also if HR at your dream company is so abusive, your dream there can quickly become a nightmare...

Remember your ambition is a different type of work, and a different type of employer, not that specific employer. Carry on preparing yourself for the work you want to do, and applying for suitable jobs.

@PatriciaShanahan , yes you are right, i should continue preparing.. Finally this morning i am thinking to call the new HR and explain all this and would like to get a written call letter for 60 days period, i would explain her that i really wanna join you and at the same time i really dont wanna ditch the former company. Well, i could go extra mile by working on weekend on the dream company in those 60 days... :) if that helps.. , lets see....

@VishwaRatna Don't think of the current potential employer as a "dream company". They have been, at a minimum, extremely inconsiderate, and no employer ever treats you better than when they are trying to hire you. You have not yet found your dream company, the one that does the type of work you want and is fair to its employees.

If you somehow get 45 days notice with your current employer, and then the new employer says "Oh, sorry, somebody told you the wrong salary, here is the correct offer letter for half your current salary" then what will you do? This "job offer" isn't worth anything until it is written down.

The "potential employer" wants him to leave his current employer early so they can use his unemployed status to manipulate him. He said himself - there is no offer letter.

need to join the company in 45 days then only we can give you offer letter. This is not clear. Do you mean "we will only hire you if you can start within 45 days"? It SOUNDS (since you know the salary) like they have already given you an offer letter and will give you a contract (now), but it has a condition of joining within 45 days

Also, do they want you to join 45 days after saying "Okay" or do they want you to join by X date? Did they explain why?

@PatriciaShanahan > EDIT(27 Aug 2019): I received the call letter with the date of Joining as 15th October. And today is 27th August and if i resign > today in my company i will be free by 27th October. Shall i ask then > to increase a date of 13 more days on the deadline. Shall i ask a > written document for that or email conversation is ok?

They are still wasting your time by assuming you can be there 45 days after giving notice. At this point I would decline the offer, reminding them that you have a 60 day notice period. Given their inconsiderate behavior, after this I would probably reject even a written offer that allows for 60 days notice. You should certainly not resign, or discuss the matter with your employer, unless and until you have a written offer allowing at least 60 days notice.

Why not just quit, tell them that you're going to be gone in 45 days, and then just go to work for the new company once the 45 days are up? What are they going to do when you don't turn up for work, fire you? Give a negative reference? You've already gotten another job!