Russian Foreign Minister Sergei Lavrov also attended the inauguration.
Ferrero-Waldner told students and professors that the EU is worried about some negative developments in the fields of democracy, human rights, and media freedom in Russia. She said she was particularly concerned after this month's contract-style killing of the investigative journalist Anna Politkovskaya.
Ferrero-Waldner also expressed concern over current tensions between Russia and Georgia.
The EU and Russia will provide equal funds to the institution, giving $3.75 million each.