Russian President Vladimir Putin and acting Georgian leader Nino Burjanadze have held talks aimed at mending ties strained by the Chechnya conflict.
Burjanadze hopes for a new chapter in relations with Moscow
After the Moscow talks, Ms Burjanadze called the visit a "breakthrough".
Mr Putin said Russia was interested in ensuring Georgia was strong, independent and self-sufficient.
Tensions between the two countries have grown recently over a number of issues, including Moscow's charges that Tbilisi is harbouring Chechen rebels.
Georgia denies the accusations, and in turn, has expressed concern over Russia's alleged backing for Georgia's rebellious regions of Abkhazia and Ossetia.
After Thursday's meeting, Ms Burjanadze thanked Vladimir Putin for inviting her to Moscow even though she was only a temporary leader.
A Kremlin source said the two sides had considered ways "to eliminate negative developments in Russian-Georgia ties".
Ties between the two sides have also been strained over Tbilisi's charges that Russia is trying to undermine its sovereignty by easing a visa regime for residents of the rebellious region of Ajaria.
The Ajarian leader, Aslan Abashidze, has already said he does not recognise the new government in Tbilisi as legitimate.
The Georgian administration was further angered by meetings between in Moscow between Russian officials and leaders of South Ossetia and Abkhazia.
Ms Burjanadze became interim Georgian leader after opposition protests forced former President Eduard Shevardnadze from office in November.
The opposition parties are fielding a single candidate, Mikhail Saakashvili, in next month's elections.