Abraham (aka Avram) Melnikov was born into a Jewish family in 1892 in Bessarabia, Russia (a historical region in modern-day Moldova and Ukraine). He studied medicine briefly before emigrating and settling in the USA, where he entered the Chicago School of Art. During the First World War, he served in Palestine with the Jewish Legion, afterwards remaining in Palestine and settling in Jerusalem, where he founded the Hebrew Artists' Association.
In 1934 Melnikov relocated to England and settled in London, where he remained for the next twenty-five years, executing portrait heads of many prominent personalities including politicians Winston Churchill, Ernest Bevin and Mordecai Eliash, and in 1937 he was commissioned by Ben Uri to make a bust of the Chairman, Adolph Michaelson. During this time he also wrote both poetry and prose. He had exhibitions at the Beaux-Arts Gallery in London in 1936 and the University of Haifa, Israel in 1982. His wife, Charlotte, was painted by both husband and wife, Julius Rosenbaum and Adele Reifenberg in the same sitting in 1945 (Rosenbaum's version is in the Ben Uri Collection), and also showed paintings at Ben Uri herself. Melnikov resettled in Haifa, Israel, shortly before his death in 1960.