"They have fulfilled the commitment" to withdraw from the area by Sept. 15 under an agreement European Union leaders reached with Russia last week, Lomaia told The Associated Press.
But he stressed that Georgia - like the West - demands a full Russian withdrawal to pre-conflict positions, in accordance with a cease-fire deal brokered by the European Union a month ago.
Adding to tension, Georgian authorities said a Georgian policeman at a post near Abkhazia was killed Saturday by gunfire that came from the direction of a position where Abkhazian and Russian forces have been based.
Russian Foreign Ministry spokesman Andrei Nesterenko confirmed the pullback in western Georgia.
"Right now the withdrawal of our peacekeeping forces is happening from these posts," Nesterenko said in televised comments.
Lomaia said some 1,200 Russian servicemen still remain at 19 checkpoints and other positions, 12 outside South Ossetia and seven outside Abkhazia. Russia said it would pull them out by Oct. 11 as long as 200 European Union observers are deployed to strips of territory surrounding the two separatist regions by Oct. 1.
Russia is pushing to keep Western monitors outside South Ossetia and Abkhazia themselves, saying the EU observers' job is to protect the regions against Georgian aggression. The United States and EU, however, want to ensure security amid high ethnic tensions following the war.
The presence of Russian troops deep in undisputed Georgian territory more than a month after the fighting ended has deeply angered Georgians and been an enormous sore point between Russia and the West.
Russia's military campaign in Georgia and its subsequent recognition of Georgia's separatist regions of Abkhazia and South Ossetia as independent nations has plunged its relations with the United States and Europe into their worst crisis since the Cold War.
An Associated Press television crew saw Russian soldiers pack military trucks before dawn Saturday with blankets and other supplies at a post by a road leading to Abkhazia province. Among the items taken down - the Russian tricolor flag.
Four trucks stood packed and ready to leave the post in the village of Pirveli Maisi, along with an armored personnel carrier.
A Russian column about the same size rolled past on a road leading to Abkhazia.
Russian forces left the two posts they had maintained for weeks on the outskirts of Poti, one by a bridge on a main road leading into the city and one a few kilometers (miles) from Georgia's main port and devastated naval base, Interior Ministry official Shota Utiashvili said.
"Russian forces have withdrawn completely from Poti," he said.
A third Russian post established more recently by the port of Poti had also been vacated, Lomaia said. He said some 250 soldiers and 20 armored vehicles pulled out of their positions and headed toward Abkhazia.
Near the de facto border with Abkhazia, an Associated Press photographer saw several small columns of Russian armor crossing a bridge leading toward the breakaway region and military trucks heading across another bridge at a separate location.
The brazen presence in Poti has been particularly galling for Georgia because it is hundreds of kilometers (miles) from South Ossetia, where the war broke out and where most of the fighting occurred.
In Vienna, confidential OSCE documents seen by The Associated Press revealed that Russian forces and their separatist militia allies were deliberately keeping OSCE monitors - who are separate from the planned EU mission - out of South Ossetia, where large numbers of Georgian homes have been looted and burned down.
Russia has also said the EU observers will not be welcome inside South Ossetia and Abkhazia, only in the strips of land surrounding them. The EU and Georgia want the observers to have access to the separatist regions themselves.
Western governments also say Moscow's plans to maintain 7,600 troops in Abkhazia and South Ossetia for the long term violates a provision in the cease-fire calling for both sides to return to positions held before the conflict erupted.
Georgian troops tried to retake South Ossetia by force on Aug. 7, but were quickly repelled by Russian tanks, troops and warplanes. The Russian military then drove deep into Georgia, occupying large swaths of territory before an initial withdrawal in late August.
The five-day war killed hundreds of people and drove nearly 200,000 people from their homes.
