Rasmussen appeared at the opening of Georgia's national parliamentary library in Tbilisi, the Russian news agency RIA Novosti reported. He called Georgia a "strong supporter of shared security," pointing to its contribution to the intervention in Afghanistan with more troops than any other NATO partner.
"Georgia's Euro-Atlantic integration will only be a matter of time," Rasmussen said.
Rasmussen repeated earlier criticism of a fence built by Russia on the border between Georgia and its breakaway region of South Ossetia. Russia has placed more than 200 miles of barbed wire fence along the border.
South Ossetia and another breakaway region, Abkhazia, have declared independence but are recognized only by Russia and a handful of other countries. Their residents now travel with Russian passports.
"Fence-building impedes freedom of movement. It can further inflame tensions. It is not acceptable and should be reversed," Rasmussen said.