In 1932, the Abramowitz family managed to leave Russia and traveled to Mandatory Palestine via Poland. At eighteen, Sasha was too old to be included in his family's entry permit and had to remain in Poland until 1934, when he received his own immigration permit. In 1945, Sasha met Niusia (Esther) Abeles and they married in Tel Aviv in 1946. Two years later, on the advice of his author friend Benjamin Tammuz, he changed his surname to Argov. Sasha and Niusia had two children, Itamar and Tali.
Sasha had initially hoped to work in the local music industry, and found occasional opportunities to accompany dancers and singers. Since he did not have a steady source of income, he decided to become a bank clerk, a position he held for 22 years. In 1957, Argov became a partner in the Russian bookstore Boleslavski in Tel Aviv, where he worked until its sale in 1989.
A few years after his arrival in Palestine, he was asked to compose songs for kibbutz celebrations and to work as an accompanist at the festivities. In the late 1940s, he wrote songs for and accompanied the Ayalon troupe of the Palmach, which toured all over the country. In 1948, he was appointed chief composer of another Palmach troupe, the Chizbatron. Almost every song in the Chizbatron's repertoire became a local hit, most notably Hareut (Friendship), which was widely regarded as a symbol of the War of Independence. During the following two decades, Argov composed material for numerous ensembles and army troupes, including the Nahal troupe, Bazal Yarok, HaTarnagolim, Gesher HaYarkon, Hahamtzitim,and HaGashash HaHiver.
Argov was especially interested in the theater and composed his initial music for the stage, in the 1930s, for kibbutz performances. Beginning in the 1950s, he composed music for productions of the Cameri, Habima and Haifa theaters, as well as for children's plays, slapstick comedy and other light entertainment. Most successful was the musical Shlomo HaMelekh vShalmi HaSandlar (The King and the Cobbler), with lyrics by Natan Alterman, adapted from Alterman translation of Sammy Gronemann's play. The musical opened in 1964 to wide acclaim, was performed hundreds of times by different troupes, and remained popular through the 1990s. Argov also composed for song festivals, poetry evenings, Israel Radio sketches, and films.
In 1994 Argov was invited to the signing of the peace treaty between Israel and Jordan. To commemorate the event, he composed Ulay Zeh Shalom (Maybe This Is Peace) to words by the poet Nathan Yonatan.
During the latter half of the 1970s, Argov worked closely with the stars of the Israeli musical firmament, including the singer Ora Zitner and the singer/composer Matti Caspi. These collaborative ventures resulted in numerous records and live shows.
Sasha Argov composed over a thousand songs to the words of Israeli poets and lyricists, such as Natan Alterman, Tirza Atar, Leah Goldberg, Haim Guri, Hayim Hefer, Omer Hillel, Rachel, Nathan Yonatan, and Natan Zach. Recognized for his sensitivity to and respect for the written word, he felt a responsibility to stay true to the meaning and rhythm of the texts he put to music. This was expressed in his melodic interpretation, the harmonic structure, and the interplay between the accompaniment and the melody.
Argov was influenced by an assortment of musical styles – classical music, European lieder, Russian folk music, French chansons, ballroom music, Latin-American music, jazz, pop and rock – and wrote in an unusually intricate musical language which combined both popular and classical elements. Although occasionally very difficult to perform, his songs were so popular that they were considered an inseparable part of the collective consciousness and Israeli identity.
During his lifetime, Argov received recognition and admiration from the public and the music world. Composers, arrangers and singers paid tribute to him, whether in recordings or events held in his honor. Even after Argov's death, artists of all ages are still performing his music.
In 1988, Argov was awarded the Israel Prize for his contribution to Israeli song. He received the ACUM (Composers, Authors and Publishers Society of Israel) prize in 1982 and the Yigal Allon Prize for Zionist Pioneering in 1985. In 1987, Argov was declared an honorary citizen of Tel Aviv.
Sasha Alexander Argov died on September 27, 1995, at the age of 81.