Georgian Defense Minister Irakli Alasania met his NATO counterparts in Brussels to discuss opportunities to join the alliance. Georgia is the largest contributor to the international military mission in Afghanistan outside the alliance.
Rasmussen said a stable and democratic Georgia is welcome as an eventual NATO member.
"Georgia will become a member of NATO provided it meets the requirements for membership," he said in a statement published Wednesday. "I look forward to a future in which Georgia is in the alliance."
Georgia was accused of selective justice after supporters of embattled President Mikheil Saakashvili were arrested on charges of abusing political office and corruption. Saakashvili was criticized for his 2008 decision to go to war with Russia over the breakaway republics of Abkhazia and South Ossetia.
Russian security forces erected a fence last week along the border with South Ossetia. Rasmussen was quoted by Russian state news agency RIA Novosti as saying he was following the development "with great interest."
Georgia holds elections later this year.