Germany invaded France, Belgium, the Netherlands, and Luxembourg on 10 May 1940. The Netherlands and Belgium were overrun using blitzkrieg tactics in a few days and weeks, respectively. The French-fortified Maginot Line and the Allied forces in Belgium were circumvented by a flanking movement through the thickly wooded Ardennes region, mistakenly perceived by French planners as an impenetrable natural barrier against armoured vehicles.
British troops were forced to evacuate the continent at Dunkirk, abandoning their heavy equipment by early June. On 10 June, Italy invaded France, declaring war on both France and the United Kingdom; twelve days later France surrendered and was soon divided into German and Italian occupation zones, and an unoccupied rump state under the Vichy Regime. On 3 July, the British attacked the French fleet in Algeria to prevent its possible seizure by Germany.
In June, during the last days of the Battle of France, the Soviet Union forcibly annexed Estonia, Latvia and Lithuania, and then annexed the disputed Romanian region of Bessarabia. Meanwhile, Nazi-Soviet political rapprochement and economic cooperation gradually stalled, and both states began preparations for war.
With France neutralized, Germany began an air superiority campaign over Britain (the Battle of Britain) to prepare for an invasion. The campaign failed, and the invasion plans were canceled by September. Using newly captured French ports, the German Navy enjoyed success against an over-extended Royal Navy, using U-boats against British shipping in the Atlantic. Italy began operations in the Mediterranean, initiating a siege of Malta in June, conquering British Somaliland in August, and making an incursion into British-held Egypt in September 1940. Japan increased its blockade of China in September by seizing several bases in the northern part of the now-isolated French Indochina.
Throughout this period, the neutral United States took measures to assist China and the Western Allies. In November 1939, the American Neutrality Act was amended to allow "cash and carry" purchases by the Allies. In 1940, following the German capture of Paris, the size of the United States Navy was significantly increased and, after the Japanese incursion into Indochina, the United States embargoed iron, steel and mechanical parts against Japan. In September, the United States further agreed to a trade of American destroyers for British bases. Still, a large majority of the American public continued to oppose any direct military intervention into the conflict well into 1941.
At the end of September 1940, the Tripartite Pact united Japan, Italy and Germany to formalize the Axis Powers. The Tripartite Pact stipulated that any country, with the exception of the Soviet Union, not in the war which attacked any Axis Power would be forced to go to war against all three. During this time, the United States continued to support the United Kingdom and China by introducing the Lend-Lease policy authorizing the provision of materiel and other items and creating a security zone spanning roughly half of the Atlantic Ocean where the United States Navy protected British convoys. As a result, Germany and the United States found themselves engaged in sustained naval warfare in the North and Central Atlantic by October 1941, even though the United States remained officially neutral.
The Axis expanded in November 1940 when Hungary, Slovakia and Romania joined the Tripartite Pact. In October 1940, Italy invaded Greece but within days was repulsed and pushed back into Albania, where a stalemate soon occurred. In December 1940, British Commonwealth forces began counter-offensives against Italian forces in Egypt and Italian East Africa. By early 1941, with Italian forces having been pushed back into Libya by the Commonwealth, Churchill ordered a dispatch of troops from Africa to bolster the Greeks. The Italian Navy also suffered significant defeats, with the Royal Navy putting three Italian battleships out of commission by a carrier attack at Taranto, and neutralising several more warships at the Battle of Cape Matapan.
German paratroopers invading the Greek island of Crete, May 1941.