- Jun 1 Glorious First of June; first naval battle between Britain (under Admiral Lord Howe) and France (Vice-Admiral Louis Thomas Villaret de Joyeuse) during French Revolutionary Wars. Britain gains tactical win.
- Jun 5 US Congress passes the Neutrality Act, banning Americans from serving in foreign armed forces
New Settlement
Jun 23 Russian Empress Catherine II (Catherine the Great) grants Jews permission to settle in Kiev

Catherine the Great
Battle of Fleurus
Jun 26 Battle of Fleurus: major victory by forces of the First French Republic under General Jean-Baptiste Jourdan over the Coalition Army (Great Britain, Hanover, Dutch Republic, and Habsburgs) first use of reconnaissance balloon
Learn More- Jun 30 Battle of Fort Recovery, Ohio