Grybauskaitė's press office said on Tuesday that the two presidents had spoken by phone.
"The conversation took place in the run-up to the NATO summit in Brussels on 25 May. President Margvelashvili requested Lithuania's support for issues of importance to Georgia at the upcoming meeting," it said in a press release.
Grybauskaitė said that "it is very important for NATO to maintain its open door policy and not to let Georgia and Ukraine, both seeking membership in the Alliance, slip from the memory of the international community".
According to the Lithuanian president, Georgia, which has experienced Russia's direct military aggression, "spares no effort to create a safe future for its people, defend and protect its sovereignty and territorial integrity".
Russia recognized independence of Georgia's breakaway regions of Abkhazia and South Ossetia after the 2008 war and maintains a permanent military presence in the regions which are regarded by the international community as occupied territories of Georgia.
NATO announced at its Bucharest summit in 2008 that Georgia would become a member of the Alliance, but the probability of this happening in the near future seems vague.