EXCLUSIVE

Mary Tyler Moore is in grave condition at a Connecticut hospital ... TMZ has learned.

Sources close to the family tell us her condition is so grim family members are coming to the hospital to say goodbye. The TV icon's long battled diabetes, and she underwent brain surgery in 2011.

One source tells us Mary has been on a respirator for more than a week.

We're told Moore is suffering from a number of health problems and recently it has become critical.

Mary starred in "The Dick Van Dyke Show" and had an incredible run with "The Mary Tyler Moore Show."