He was elected to the Federal Council on 10 December 1940 and handed over office on 31 December 1954. He was affiliated to the Free Democratic Party.
During his time in office he held the Military Department. On 2 December 1944 Kobelt contacted Brigadier General B. R. Legge related to internees, among others in the Wauwilermoos internment camp near Luzern. Kobelt was President of the Confederation twice in 1946 and 1952.
- Dwight S. Mears (2010). "Interned or Imprisoned?: The success and failures of international law in the treatment of American internees in Switzerland, 1943-45". University of North Carolina at Chapel Hill. Retrieved 2015-10-25.
- Steiner, Die Internierung von Armeeangehörigen kriegfuhrender, 66. Memo from Swiss military minister Karl Kobelt to Brigadier General B. R. Legge, number 8211.117.N/G, dated 2 December 1944, NARA, RG 84, E3207. Tribunal panel requirements Art. 12, 13, & 107; SFA, Ref. No. 10 014 517, "Militärstrafgerichtsordnung (Bundesgesetz vom 28. Juni 1889)", Bundesblatt 1889, Band 3, Heft 37[permanent dead link]. Data on military tribunals conducted against Americans were referenced from Bern Archives, SFA Box E 5330-01 1975/95. 93 Art. 3, Section 2 of the Military Penal Code: SFA, Ref. No. 10 030 071, Militärstrafgesetz Bundesgesetz vom 13 Juni 1927, Bundesblatt 1927, Band 1, Heft 25[permanent dead link]
- M. Brawand (1944). "120/4986 - Interpellation Brawand. Interniertenlager Wauwilermoos" (PDF) (in German). eda.admin.ch. Retrieved 2015-10-25.
- Karl Kobelt in the Dodis database of the Diplomatic Documents of Switzerland
- Profile of Karl Kobelt with election results on the website of the Swiss Federal Council.
- Karl Kobelt in German, French and Italian in the online Historical Dictionary of Switzerland.
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