In the 1990s, Cotti led the Swiss government's unsuccessful attempts to further Switzerland's political integration into the European Union.

[3] Cotti was elected to the Federal Council of Switzerland on 10 December 1986, succeeding Alphons Egli, and resigned on 30 April 1999.

[3] In this and other areas, Cotti's visions proved incompatible with Switzerland's complicated and slow consensus politics, which earned him the nickname of "minister of announcements" (Ankündigungsminister).

[5] Cotti also prominently represented the country abroad, gaining international recognition as the first Swiss president of the OSCE.

[3] After retiring from politics, Cotti served in leading advisory positions in major Swiss companies, including on the board of Credit Suisse.