According to him, Moscow and Tbilisi recently succeeded in solving the most complicated bilateral problem - the withdrawal terms of the Russian military bases from Georgia.
"We are carrying out constructive dialogue on the Abkhaz and South Ossetian settlement," the parliamentarian said.
It will help the sides complete drafting the big treaty and hopefully sign it, he added.
After that, Russia and Georgia will be able to discuss simplification of visa regulations, Kosachev said.
Abkhazia and South Ossetia are two self-proclaimed republics in Georgia.
There are two Russian military bases on Georgia territory, in Akhalkalaki and Batumi. The decision on their withdrawal was made at the summit of the Organization for Security and Cooperation in Europe in Istanbul in 1999. The sides agreed to withdraw bases step-by-step. In 2005, all military facilities except the bases proper will be handed to Georgia. In 2006, military hardware will be withdrawn from Akhalkalaki (near the Armenian border). The base will be closed in 2007. Military hardware will be pulled out from Batumi (a port on the Black Sea) in 2008. After that, the base will be closed.