Give my regards to your family!
'Salutami' — sa-LU-ta-mi. Stress on the second syllable. Imperative of 'salutare' + 'mi'. 'Familia' — fa-MIL-ia.
Use as a warm parting phrase that extends your goodbye to include the other person's absent family members. Very common and deeply Italian — it shows social breadth.
'Salutami' is the imperative of 'salutare' (to greet) + indirect object 'mi' (for me). 'Salutami la tua famiglia' = 'greet your family for me'. This extends the social connection beyond the immediate goodbye — your warmth travels with them.
Salutami i tuoi!
Give my regards to your people!
'I tuoi' (yours = your people) — informal, warm. Refers to family collectively.
Manda i miei saluti a Marco.
Send my regards to Marco.
Specific person — names them to show you remember them personally
Di' a tua madre un grosso abbraccio da parte mia.
Give your mother a big hug from me.
Most warm — a physical hug transmitted through the person. Typically between women.
Sending regards to someone's family ('saluta la famiglia') is a deeply Italian social ritual that acknowledges the family as the primary social unit. Even if you've never met the family members, including them in the goodbye acknowledges their importance in the person's life.