Phillips, whose twin sister Esther wrote the rival "Ask Ann Landers" column, died in Minneapolis on Wednesday after a long battle with Alzheimer's disease.
"I have lost my mother, my mentor and my best friend," daughter Jeanne Phillips said in a statement released by the syndicator of the "Dear Abby" column, Universal Uclick.
"My mother leaves very big high heels to fill with a legacy of compassion, commitment and positive social change. I will honor her memory every day by continuing this legacy," Jeanne Phillips added
Phillips' family announced in August 2002 that she had been diagnosed with Alzheimer's disease.
Phillips had brought daughter Jeanne in to collaborate on the syndicated newspaper column in 1987 and in December 2002 turned over all responsibility for it to her.
(Reporting By Eric Kelsey; Editing by Sandra Maler)
(This story corrects name of her sister's column in 2nd paragraph)