In 1958 he was a head of Georgian delegation to World Fair EXPO in Brussels, Belgium and in 1967 in Montreal, Quebec, Canada.
In 1961 Givi Javakhishvili was heading the delegation of Georgian SSR in Moscow at Congress of the CPSU where he gave the famous speech demanding the removal of Joseph Stalin's body from Lenin's Mausoleum.
By his direct initiative many high-profile buildings were built in Georgian capital Tbilisi, such as State Philharmonic Hall and the Palace of Sport.
He inaugurated an opening of Tbilisi Metro in 1966 which had become the fourth underground rail system in the Soviet Union.
He also hosted high-profile foreign guests in Tbilisi, such as Indian Prime Minister Jawaharlal Nehru, Queen of Denmark Margrethe II, French President Georges Pompidou, Shah of Iran Mohammad Reza Pahlavi, Cuban leader Fidel Castro and many other prominent figures of the 20th century.