In the middle of a novel published in the Soviet Union in 1981, two young people are exchanging opinions about Russian poetry. After several names have come up, one asks the other, “And how about Yevtushenko?”, to which he gets the reply: “That’s another stage that’s already past.” An unremarkable exchange, of course, save that the novel (Wild Berries) was by the poet Yevgeny Yevtushenko himself.

It indicates several things about Yevtushenko, who has died aged 84: his unquenchable self-regard, his ability to laugh at himself, his appreciation of the vagaries of fame. It also reminds us that there was a brief stage when the development of Russian literature seemed almost synonymous with his name.

Notoriety of a political sort first came Yevtushenko’s way in 1956, with the publication of his narrative poem Zima Junction, which encountered heavy criticism. The poem had no anti-Soviet message, but touched on tender spots, such as confusion over the direction of the country after Stalin, that Soviet writers had mostly avoided. It provoked outrage in sections of the Soviet press.

But his fame was secured by the publication in 1961 of what must be the poem of the 1960s, Babi Yar. It derived from his visit to a ravine near Kiev where the Nazis had perpetrated a massacre 20 years before. The poet’s wholehearted identification with the Jewish victims made the work one of the most stirring calls ever against antisemitism. Its prestige was redoubled when Shostakovich set it as the opening movement of his 13th Symphony (1962); four other Yevtushenko poems were the basis for its other movements, making a cumulative portrait of the mood of the times. The public impact was huge.

Yevtushenko was from early on obsessed with travel, first within the USSR and then, as invitations came in from abroad, anywhere in the world he could manage to get to. By 1962 he had become a celebrity outside Russia, and featured on the cover of Time magazine. His many public readings in the west were packed, and a slim volume of translations became the biggest-selling book of foreign poetry in English. He sought out meetings with famous people – TS Eliot in London, Robert Kennedy in the US – not just for name-dropping purposes, but to see for himself the makers and movers of the modern world.

In 1963 came a crisis year in Soviet literature, when the authorities tried to get a grip on the incipient pluralism represented by many artists and writers, without resorting to out-and-out repression. Early that year Yevtushenko was in Paris, where the magazine L’Express commissioned his A Precocious Autobiography: the risk was astonishing, since to publish a full-length work, touching on sensitive subjects, for a specifically western readership and without submitting it to Soviet censorship could be (and by some was) taken as treachery. The autobiography gave a vivid picture of his anarchic youth and a memorable set-piece account of the death in 1953 of Stalin.

The anti-modernist offensive occasioned some bizarre meetings between Soviet officialdom and writers or artists. When Nikita Khrushchev attacked the modernist sculptor Ernst Neizvestny with the proverb “Only the grave can correct a hunchback”, Yevtushenko retorted: “I hope we have outlived the time when the grave is used as a means of correction.” Khrushchev described Yevtushenko as “ungovernable”.

Yevtushenko never stopped writing poems long or short; though their impact diminished, his books continued to sell in huge editions. But his restless talent began to seek other outlets. From the 1950s onwards, he had written stories and journalistic pieces; prose took a growing place in his work, with the novels Wild Berries and Don’t Die Before You’re Dead (1993) intimately connected with their times. He got involved in theatrical productions derived from his works, then in films.

With the dissolution of the Soviet Union, he again found himself occupying a prominent public position. He was elected to parliament for Kharkov, northern Ukraine, in 1989, and espoused worthy causes: women’s rights, the ecological threat to Lake Baikal, the need for a monument to Stalin’s victims opposite the Lubyanka. But though he kept one foot in Russia, his other was placed in the US midwest, where he could earn a living through college teaching, chiefly at Tulsa University, Oklahoma, and where he made his chief home in later years.

Russian literature, however, was never far from his attentions. Through the perestroika period he had been publishing (in the journal Ogonyok) a huge monthly anthology of modern Russian poetry, and this eventually found expression in English through a plump volume of translated verse, Twentieth Century Russian Poetry (1993). Various honours came his way, but he turned down membership of the Russian Order of Friendship in protest against the suppression of Chechen autonomy. He was vice-president of Russian PEN, 1990-93.

Yevtushenko was born in Zima, a small town west of Irkutsk in Siberia. He took the surname of his mother Zinaida’s family, who were of Ukrainian origin. His father Aleksandr’s family were intellectuals with the Latvian name Gangnus; his forebears included Russians and Tatars. When his parents separated, he went with his mother to Moscow, then was evacuated back to Zima in 1941, returning to Moscow in 1944. He did not see Zima again until the summer of 1953, the time of public and personal crisis just after the death of Stalin that formed the background to the poem Zima Junction.

From childhood on, he was not only a voracious reader (inspired by his father), but a precocious versifier, first published in the journal Soviet Sport in 1949. He went on geological expeditions to central Asia in his teens, and was a considerable athlete, with ambitions towards becoming a professional footballer. He was simultaneously a copious, if indiscriminate, poet, and produced his first book in 1952. This gained him entry to the Moscow Literary Institute, from which – always self-willed and rebellious – he was slung out without graduating. No matter: by the end of his 20s he had produced nine collections of poems and developed the particular mix of public and private themes, often in a single work, that he made so much his own.

Among his contemporaries it was probably the intimate side of his work that brought him popularity: it was fresh, forthright, lyrical, from an unashamedly youthful heart. He and some of his contemporaries became known to a mass audience not just through publications but through ever-larger public readings. He had tremendous stage presence, and could be a charismatic figure in public and private; he also pursued an enthusiastic love life.

He married the brilliant poet Bella Akhmadulina in 1955, when she was 18. They soon divorced, and thereafter he notched up a marriage a decade until his 50s (to a fellow Siberian, Galina Sokol, in 1962; to the English translator Jan Butler in 1978; and to Maria Novikova, who survives him, in 1986) and had five sons; he recalled all his wives with affection in his 1998 memoir Marked Papers.

Yevtushenko was a protean figure, larger than lifesize, not nearly as transparent as his self-revelatory, straight-talking persona would suggest, often ambiguous in his public roles. Sovietologists concluded early on that he had sold out to the regime. This was nonsense: his self-judgment (in the 1960 poem Conversation) stands: “I did no more than write, never denounced; / I left out nothing I had thought about / ... doing what anyhow had to be done.”

He knew his limitations: “I shall be happy if just one of my lines helps someone of later generations.” He owed much to Vladimir Mayakovsky, Boris Pasternak (whom he knew), Sergei Yesenin and others, not always comparing well with his models. But he was a considerable poetic technician, whose command of rhyme, rhythm and rhetoric were prime strengths; even his weak poems have memorable lines.

Other poets acknowledged his power – the fastidious Joseph Brodsky claimed to know several hundred lines of his by heart. He risked the contempt of pundits with his combination of sharpness, sentiment, populism, self-confidence and sheer enjoyment of the sound of language (like the Liverpool poets and similar performance poets, whom he helped to inspire). An important part of his achievement was to “democratise” poetry, giving it emotional punch at the expense of refinement. As far as he was concerned, “poetry and life are the same for me”. His constant inquisitiveness went with a great gift for friendship: his was above all a generous spirit.

• Yevgeny Aleksandrovich Yevtushenko, writer, born 18 July 1932; died 1 April 2017