The senator is taking part in the World Economic Forum in Davos. On Thursday he held a bilateral meeting with Georgia's elect President Mikhail Saakashvili as part of the forum.
"We agreed that both Georgia and Russia need positive changes in bilateral relations," Margelov said.
According to him, the Georgian President confirmed that he would pay the first official visit to Russia. However, after the inauguration ceremony, he is to go to Strasbourg to address a session the Parliamentary Assembly of the Council of Europe.
Saakashvili invited Margelov to visit Georgia.
"We shall discuss this invitation at a meeting of the Federation Council. Certainly, we should improve our relations," Mikhail Margelov said.
"We need neither pro-American, nor pro-Turkish and pro-Russian government in Georgia. We need a pro-Georgian government," he noted.
Some days ago Mikhail Saakashvili said that Georgia would like to join the Eurasian Economic Community /Russia, Belarus, Kazakhstan, Kyrgyzstan and Tajikistan". According to the President, it could be a very important event in bilateral relations.
Saakashvili and Margelov also discussed regional security.
"We shall solve the problem of Russian military bases in Georgia together in accordance with the international law," Margelov said.