More satisfying was his finely toned performance as Tevye the milkman in Fiddler on the Roof, whom he played more than 2,000 times all over the US. Although Zero Mostel originally created the part on Broadway in 1962, and Topol played it in Norman Jewison’s 1971 film, for US theatregoers Bikel became identified as much with the role as Yul Brynner was with The King and I. Bikel, who criticised Mostel for his “improvised shtick”, based Tevye on his grandfather, who had “a similar lively relationship with God”.

Nevertheless, Bikel considered the musical, based on stories by the Yiddish writer Sholem Aleichem, “a charming show, but shtetl lite”. Thus there was more sense of tragedy in his one-man show Sholem Aleichem: Laughter Through Tears (2008), in which he sang in English and Yiddish, and in the documentary Theodore Bikel: In the Shoes of Sholem Aleichem (2014).

Apart from Fiddler on the Roof, the other Broadway musical with which Bikel was associated was The Sound of Music (1959-63), in which he created the role of Captain von Trapp (played in the film by the more handsome Christopher Plummer). During the out-of-town tryouts for the hit musical, Richard Rodgers and Oscar Hammerstein felt that the captain should have a song that bids farewell to the Austria he loved. Using Bikel’s guitar-playing and folk-singing talents, they wrote Edelweiss. The simple, patriotic song in waltz time ends with the line: “Bless my homeland for ever.”   However, Bikel had little cause to bless his homeland. Born in Vienna, he fled with his family to Palestine after the Nazi invasion in 1938. His father, an insurance salesman and ardent Zionist, named his son after Theodor Herzl, one of the founders of Zionism. Bikel, who began acting in his teens, providentially made his professional stage debut as a Tsarist village clerk in Tevye the Milkman (1943), based on Aleichem, at the Habimah theatre in Tel Aviv, after which Bikel co-founded the city’s Cameri theatre a few years later.

In 1946, Bikel went to London to study at Rada (Royal Academy of Dramatic Art) before getting small roles on the West End stage. One of them happened to catch the attention of Michael Redgrave, who recommended him to Laurence Olivier, at the time directing the first UK production of Tennessee Williams’ A Streetcar Named Desire (1949). Bikel was praised in the difficult role of Mitch, the sensitive mother’s boy, who awkwardly courts Blanche Dubois (Vivien Leigh).   His other London stage success was as the Russian colonel in Peter Ustinov’s satire The Love of Four Colonels (1951).

At the same time, Bikel’s film career began with John Huston’s The African Queen (1951) where, at the climax on board ship, he is the unflinching German naval officer prepared to hang Humphrey Bogart and Katharine Hepburn for spying. Huston cast him again in Moulin Rouge (1952), in which Bikel has a short scene as King Milo IV of Serbia (miswritten Milan IV on his calling card), one of the first people to buy a painting by Toulouse-Lautrec (José Ferrer). Bikel then cropped up briefly in British war films as a Dutch prisoner in The Colditz Story (1955), and a German officer in Above Us the Waves (1955).

He continued in much the same way, but in bigger parts, when he went to Hollywood after appearing on Broadway in Tonight in Samarkand (1955) as a French police inspector opposite Louis Jourdan. In The Enemy Below (1957), Bikel is the sympathetic second-in-command on a U-boat in the second world war, being hunted by the American captain (Robert Mitchum) on a destroyer.

For Stanley Kramer, Bikel played a sadistic French general ordering the execution of rebel Spaniards (including Frank Sinatra) during the Napoleonic wars in the absurd, overblown epic The Pride and the Passion (1957) and an American at last in The Defiant Ones (1958). Bikel was delighted to be given the role of the sheriff in pursuit of two escaped convicts chained together (Tony Curtis and Sidney Poitier), for which he had an impeccable southern accent. Of his Oscar-nominated performance, the New York Times noted: “In the ranks of the pursuers, Theodore Bikel is most impressive as a sheriff with a streak of mercy and justice, which he has to fight to maintain against a brutish state policeman.”

Back to foreigners, Bikel was effectively slimy as a Greek fifth-columnist pitted against foreign correspondent Mitchum in 1941 before and after the German invasion of Greece in Robert Aldrich’s The Angry Hills (1959). However, perhaps his best remembered film role, albeit a very short one, was as the phonetics expert Zoltan Kapathy, who hopes to expose Eliza Doolittle (Audrey Hepburn) as a fraud in My Fair Lady (1964), but finally declares her not only Hungarian but of royal blood. Kapathy is later described by Professor Higgins (Rex Harrison) as that “hairy hound from Budapest. Never leaving us alone. I’ve never known a ruder pest!”

Bikel won the role of the Russian captain of a submarine that accidentally runs aground on the New England coast in The Russians Are Coming, The Russians Are Coming! (1966), because he was able to play a convincing Russian speaker. Off the beaten track, Bikel found himself in 200 Motels (1971), a surrealistic vision of life on the road for Frank Zappa and his band Mothers of Invention. As government agent Rance Muhammitz, Bikel is a satanic figure who wanders around dispensing hamburgers from a fuming briefcase.

Meanwhile, Bikel had a parallel career on television, appearing mainly as eastern Europeans in series such as Ironside, Charlie’s Angels, Falcon Crest and Star Trek: The Next Generation. Another side to his life arguably brought him more fame than acting. From 1955, Bikel recorded many albums including Jewish and Russian folk songs backed by him on acoustic guitar. In 1959, he co-founded the Newport Folk festival, where he often teamed up with Bob Dylan, Pete Seeger, Peter, Paul and Mary and Joan Baez.

In the 1960s, Bikel became increasingly involved with civil rights causes – he was arrested protesting against the Vietnam war – and was an activist for the Democratic party. His offstage activities included his hands-on presidency of Actors’ Equity (1973-82), and of the Associated Actors and Artistes of America from 1988. Among his other interests were keeping the Yiddish language alive and his love of Israel, though not an uncritical one.

Bikel is survived by his fourth wife, Aimee Ginsburg, whom he married in 2013, and two sons, Robert and Daniel, from his second marriage, to Rita Weinberg Call. That and his first marriage, to Ofra Ichilov, ended in divorce. His third wife, the conductor and pianist Tamara Brooks, died in 2012.

• Theodore Meir Bikel, actor, singer and political activist, born 2 May 1924; died 20 July 2015