On his return to Japan, Ōsumi was promoted to commander, and was assigned as aide-de-camp to Fleet Admiral Tōgō Heihachirō. He spent a year as executive officer on the battlecruiser Tsukuba from 1913–1914, returning to staff positions until 1 December 1917, when he received his first command: the battleship Asahi.
From 1 December 1918 – 1 July 1921, Ōsumi was appointed as military attaché to France. During that time, he was a participant in the Japanese delegation to the Versailles Peace Treaty negotiations. Also during this period, on 1 December 1920, he was promoted to rear admiral.
After his return to Japan, Ōsumi served as Director of the Bureau of Naval Affairs in 1922, and was promoted to vice admiral in 1924, Vice Minister of the Navy in 1925, commander-in-chief of the IJN 2nd Fleet in 1928, and Commander in Chief of the Yokosuka Naval District in 1929. He was promoted to full admiral on 1 April 1930. Ōsumi was a strong proponent of Japan's southward expansion, but refused to align himself with either the Treaty Faction or the Fleet Faction within the Navy. He was awarded the Order of the Sacred Treasures, 1st class on 14 May 1931.
Ōsumi served as Minister of the Navy from December 1931-May 1932, under the short-lived second cabinet of Prime Minister Wakatsuki Reijirō.