Kuznetsov was born in Sofilovka, Kostroma Province, Russian Empire. He joined the communist party in May 1927. He took a break of his studies of engineering when he went to the United States for metal processing studies from 1931 to 1933.Kuznetsov held a variety of government and Communist Party positions beginning in 1940. He was a Chairman of the Soviet of Nationalities 12 March 1946–12 March 1950. In 1955 he became first deputy minister of foreign affairs. On 7 October 1977 he was elected First deputy chairman of the praesidium of the USSR Supreme Soviet.