The message was published on the website of the Ministry of Foreign Affairs.
Ryabkov stressed that Moscow expects that Tracy will strictly follow the requirements of Russian laws in his activities, as well as observe the norms, customs and not interfere in the internal affairs of Russia.
Earlier, the new American ambassador arrived at the Russian Foreign Ministry to present copies of her credentials.
Protesters opposed to US policy were waiting for her near the entrance.
About half an hour later, she left the building without comment.