Under the Swiss system of a rotating, non-executive presidency, Calmy-Rey is both head of state and foreign minister.
At her talks with Russian Foreign Minister Sergei Lavrov, the sides will discuss bilateral political ties and several areas of practical cooperation, as well as key international issues, the Russian Foreign Ministry's spokesman said.
"The considerable overlap in opinions held by Russia and Switzerland on most global and regional problems provides a strong foundation for the countries' cooperation through international organizations and forums," Mikhail Kamynin said.
A memorandum on encouraging Russo-Swiss cooperation is expected to be signed during the visit.
President Vladimir Putin will meet with Calmy-Rey on November 9, on the last day of her visit.
