The regions, Abkhazia and South Ossetia, have declared independence, but that is recognized only by Russia and a handful of other countries. Both depend heavily on Russian economic aid and military support.
Speaking to journalists, Georgian President Mikhail Saakashvili reiterated accusations that Russia wants to drive him from power.
He said he would sign an agreement with Russian President Dmitry Medvedev to resign "if Russia is prepared to return to Georgia control of the territory it occupies ... and pull out its troops."
The prospect of Russia withdrawing troops or otherwise diluting its influence in the two regions appears all but nonexistent. In addition, Abkhazia and South Ossetia vehemently oppose any restoration of Georgian government control.
The two regions threw off most Georgian control in separatist wars in the 1990s, but Georgian authorities retained control of swaths of South Ossetia and a small piece of Abkhazia until the 2008 war with Russia. The war began when Russia, which had peacekeeping troops in South Ossetia, sent in massive reinforcements and Georgian forces launched a bombardment of the South Ossetian capital.
Animosity between the Kremlin and Saakashvili was already high before the war, centering on Saaskashvili's push to join NATO and take Georgia out of Moscow's sphere of influence. Since the war, Saakashvili has been anathema to Russia.
Medvedev, in an interview broadcast live on national television Thursday, called Saakashvili "a nobody, a zero. Sooner or later he will go into political history and we are prepared to form relations with any other leader of the country that appears, restore diplomatic relations, go as far as they are prepared to go."
Deputy Georgian Foreign Minister Nino Kalandadze expressed regret that Medevedev "is speaking in a form that's inappropriate for him and using an unsuitable lexicon."
Associated Press writer Jim Heintz in Moscow contributed to this story.