When Konenkov visited the house of the art collector Ivan Morozov, an eye-witness account says he was very dismissive: He claimed that the works by Maurice Denis, Manet, Degas and Aristide Maillol were rubbish.

[3] In 1922 Konenkov married Margarita Ivanovna Vorontsova,[a] and in 1923 they travelled to the United States to take part in the Russian Art Exhibition,[7] which was held in 1924 at the Grand Central Palace.

During the American period, Konenkov created a large body of work focusing on Bible themes, notably the Apocalypse.

He "had found favor enough with the regime to be asked to design a plaque commemorating the first anniversary of the October Revolution on the Senate Tower of the Kremlin.

"[12] Konenkov created sculptures of Aleksandr Pushkin, Anton Chekhov, Leo Tolstoy, Fyodor Dostoyevsky, Ivan Turgenev, Vladimir Mayakovsky, Konstantin Tsiolkovsky, Vasily Surikov, Johann Bach, Paganini, to name a few.

Konenkov received numerous Soviet awards, including the golden star of the Hero of Socialist Labour, the order of Lenin and the title Peoples artist of the USSR.