June 1 - Ethiopia experiences its most devastating earthquake of the 20th century, with a magnitude of 6.7. The town of Majete is destroyed, 45% of the houses in Karakore collapse, 17 kilometers (11 mi) of the main road north of Karakore are damaged by landslides and fissures, and 5,000 inhabitants in the area are left homeless.
June 4 - Vienna summit: John F. Kennedy and Nikita Khrushchev meet during 2 days in Vienna. They discuss nuclear tests, disarmament and Germany.
June 16 - Russian ballet dancer Rudolf Nureyev requests asylum in France while in Paris with the Kirov Ballet.
- A Paris-to-Strasbourg train derails near Vitry-le-François; 24 are killed, 109 injured.
- The New Democratic Party of Canada is founded with the merger of the Cooperative Commonwealth Federation (CCF) and the Canadian Labour Congress.
June 19 - The British protectorate ends in Kuwait and it becomes an emirate.
June 22 - Moise Tshombe is released for lack of evidence of connection to the murder of Patrice Lumumba.
June 23 - Antarctic Treaty comes into effect.
June 25 - Iraqi president Abdul Karim Kassem announces he is going to annex Kuwait.
June 27 - Kuwait requests British help; the United Kingdom sends in troops. (source: Wikipedia)