It si simple to understand that:
"6 days/week, not every week ( in a month) is less than 6 days/week."'
You have posted that:
"I have submitted my resignation on mail which company has accepted on mail and in acceptance only they have said I can be releived on 14th July. On which I reverted with my notice period and have also indicated on my gratuity. Then HR head has replied on the mail saying my relievign is as per company process and gratuity claim will be seen as per merit basis. I do mentioned about my notice period in the same mail conversation......................As per HR, company will pay me the unserved notice period's pay too. "
There are decisions that resignation can not accepted before expiry of notice period.
Employee can reject the offer of employer to tender notice pay in lieu of notice period.
You can claim the break is artificial and caused so as to avoid payment of Gratuity.
Beyond this if you are still unable to resoilve then you may engage a very able consel specializing in labor/service matters.