After his graduation from the Law School of Kyoto Imperial University, he entered the Home Ministry.
Omura Seiichi served as Governor of Nagano Prefecture from 15 January 1935 to 13 March 1936, and again for a second term from 11 January 1938 to 23 December 1938. He was then appointed Governor of Kanagawa Prefecture from 23 December 1938 to 4 September 1939. Later in 1939, he was Vice Minister for Education under Prime Minister Abe Nobuyuki. In 1943, he was made chairman of the Japan Student Services Organization.
After the end of World War II, during the American occupation of Japan, Omura served as Home Minister in the first Yoshida administration from 22 May 1946 to 24 May 1947. He was also appointed to a seat in the House of Peers in the Diet of Japan.
From 10 December 1954 to 19 March 1955, Omura served as Director-General for the Japan Defense Agency under the first Hatoyama administration.
Omura subsequently was elected a seat in the Lower House of the Diet from his native Okayama, and served for six terms from 21 November 1960 to 23 October 1963.