Nogovitsyn told a news conference in Moscow that "according to the peace plan, the withdrawal of Russian peacekeepers and reinforcements has begun".
The general said that Russian forces were leaving Gori and pulling back to South Ossetia and security zone defined by a 1999 agreement.
However, Georgia's foreign ministry accused Russia of violating the ceasefire by continuing military operations and failing to withdraw its troops.
"The Russian side is gravely violating the conditions provided for by the peace accord signed by the presidents of Georgia, France and the Russian Federation," it said in a statement.
The ministry cited new operations by Russia on Monday, including the re-occupation of a military base in Senaki in the west of the country where explosions were heard.
It also accused Russia of a "persistent delay in the withdrawal of its forces from Georgia".
Shota Utiashvili, Georgia's interior ministry spokesman, said that Russian forces had blown up the runway.
Tanks and armoured personnel carriers could also be seen moving freely around the strategically important city of Gori, about 60km from the capital Tbilisi, and Russian troops were controlling access.
Withdrawal commitment
The United States on Monday called on Russia to withdraw its forces from Georgia "without delay".
"If it [Russia] rolled in after August 6th, it needs to roll out," Gordon Johndroe, a White House spokesman, said. "That would be in keeping with the Russian commitment on withdrawal."
Russian tanks and armoured personnel carriers rolled into the breakaway Georgian region of South Ossetia on August 7 after the government in Tbilisi ordered a bombardment in an attempt to reassert its control.
A French-drafted six-point peace pact requires all forces in Georgia to withdraw to positions held prior to the conflict.
Sergey Ryabkov, Russia's deputy foreign minister, told Al Jazeera on Monday that his country was adhering to the ceasefire.
"We are fulfilling our obligations to the very last letter. All the briefings which our general staff give simply show we are very, very sincere in our intentions," he said.
"We definitely need to see the situation on the ground is secured and this will require Russian peacekeeping forces.
"I am not going to pour gas on the fire. I am only asking that the leadership in Tbilisi do not show anymore provocation. At the moment we see a distinct lack of this."
Missile deployment
Meanwhile, a US defence official said Russia had moved short-range SS-21 missiles into South Ossetia, possibly putting Tbilisi, the Georgian capital, in range.
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Medvedev hailed the 'heroes' of the military operation in Georgia [AFP]
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Nazanine Moshiri, Al Jazeera's correspondent on the North Ossetian, South Ossetian border, said: "There were reports on Friday that SS-21 missiles are now deployed on the outskirts of Tskhinvali [the South Ossetian capital]. There is no sign of a withdrawal here."
Nogovitsyn disputed the claim, saying Russia "sees no necessity" to place SS-21s in the region.
In Vladikavkaz, near the border with South Ossetia, Medvedev gave medals to 30 soldiers and servicemen involved in the conflict.
"It has been only 10 days since you faced a cowardly aggression," he said, standing on a drill square in front of soldiers and officers he called "heroes".
"I am sure that such a well-done, effective and peacemaking operation aimed at protecting our citizens and other people will be among the most glorious deeds of the Russian military."
Nato meeting
Meanwhile, Condoleezza Rice, the US secretary of state, arrived in Brussels to meet Nato allies to discuss the situarion in Georgia and the alliance's dealing with Russia.
Nato foreign ministers will meet on Tuesday, at Washington's request, to seek a common position on the Georgia situation and reaffirm their solidarity with Tbilisi.
Rice has accused Moscow of using "disproportionate force" against its neighbour, whose hopes to joining the military alliance have angered Russia.
She will continue on to Warsaw later Tuesday where she will sign a deal on installing a missile defense shield pact with Poland, a move sure to further increase tensions with Russia.
The Organisation for Security and Cooperation in Europe (OSCE) said on Monday that it had failed to agree on whether to send observers to Georgia but insisted that discussions were continuing.
"No agreement has been reached so far. Consultations are continuing" said Aleksi Harkonen, the representative of the OSCE's Finnish chairmanship.
The lack of agreement was largely due to the Russian delegation, Harkonen said, speaking of "the people who are actually in control of those areas" hit by the conflict in South Ossetia.