According to Timatic, the resource used by airport staff, yes, must be a minimum of 6 months.
Rules of validity of the document: passports and other documents are accepted for
the entry must be valid for a minimum of 6 6 months from the date of arrival.
The Tatkaal passport service can be used to obtain passports urgently out of turn. They are sent within one business day if police verification is not required, if it is on the third business day.
You can submit your request through the electronic Form or in person, the linked page has a rate calculator and the forms necessary to use this service.