The diplomat said this on the sidelines of the Council of Foreign Ministers of the North Atlantic Alliance.
"We are ready to close the borders if necessary," RIA Novosti quoted Tsakhna as saying.
Earlier, Finnish Prime Minister Petteri Orpo said that the Finnish authorities were closing all checkpoints on the border with Russia for asylum seekers until December 13.
Russian Deputy Foreign Minister Alexander Grushko said that the decision of the Finnish authorities to close the border with Russia will harm Finnish citizens.
Later, the Lithuanian Ministry of Internal Affairs noted that Lithuania does not see the need to close all checkpoints on the border with Russia following Finland.