Kleit was active in the anti-Tsarist revolutionary movement, and the anti-German underground between 1915 and 1918. After World War I he was elected as the Socialist vice-president of the Vilna Kehilla. Kleit left Lithuania for political reasons and lived in Berlin, Cairo, Tel Aviv, Southern France and Toronto. With the assistance of Yaakov (Yankel) Pat, the international Bundist leader, Kleit went to the United States in 1927 and there worked as a teacher in the Arbeter Ring schools until his death.
During and after World War II, Kleit worked to rescue Jews from the Holocaust and to bring survivors into the United States from Cuba and possibly other countries. There is some evidence to indicate that the circle of groups and individuals included Hashomer Hatzair, returning war veterans, non-Jewish pilots and engineers and (with inconclusive evidence) mobsters such as Meyer Lansky and (somewhat questionably) Lucky Luciano.