The term I am familiar with prior to that was "immediate family" (as opposed to "extended family").

You come across the term a lot in old genealogy books. For instance in "The History and Genealogy of the Prentice, Or Prentiss Family" (from 1883) contains:

> All his immediate family, himself, wives, and children, are dead.

https://www.google.com/books/edition/The_History_and_Genealo...