"Right now there is an ethnic cleansing of Georgians in Abkhazia," Saakashvili said in an interview on CNN.
"They are menacing the capital" of Tbilisi and "undermining ... the Georgian government" to ultimately depose it, he said. "They should hear Georgia will never surrender" because democracy "is stronger" than Russian bombs.
Georgian officials also accused Russian forces of expanding their military action to the western part of the country, saying troops moved into the town of Senaki, located near Abkhazia, Voice of America reported.
If the reports are true, the Russian military action near the second republic would indicate an increase the fighting that began last week when Georgian forces attacked the capital of the separatist province of South Ossetia, also with ties to Russia, to reassert control over the area.
The attack prompted a Russian military response called "disproportionate" by Western nations that have been appealing for an immediate halt to the fighting.
Georgian officials also accused Russian troops of seizing control of the central Georgian town of Gori, near South Ossetia. Moscow officials denied Russian troops are in the town.
Saakashvili accused Russia of trying to take over all of Georgia.
South Ossetia and Abkhazia, both with historic ties to Russia, declared independence from Georgia in the mid 1990s. Saakashvili has vowed to bring both regions back into the fold.