Putin's spokesman Dmitry Peskov said: "War started today in South Ossetia when Georgia attacked Russian peacekeepers in the disputed region."
Earlier an official in Georgia's National Security Council said Russia invaded Georgia.
Kakha Lamaia said: "If it's not war, then we are very close to it. The Russians have invaded Georgia and we are under attack."
Georgian President Mikhail Saakasvili told CNN: "Russia is fighting a war with us in our own territory.
"This is a clear intrusion on another country's territory. We have Russian tanks on our territory, jets on our territory in broad daylight."
Saakashvili accused its neighbor of a "well-planned invasion" and called on reservists to sign up for duty. He said "150 Russian tanks, armoured personnel carriers and other vehicles" had entered South Ossetia.
The president of the Georgian breakaway region, Eduard Kokoity, was quoted as saying: "About 1,400 people have died. We will check these figures, but the order of the numbers is around this. We have this on the basis of reports from relatives."
Witnesses claim Tskhinvali is devastated. "I saw bodies lying on the streets, around ruined buildings, in cars," said one.
"It's impossible to count them now. There is hardly a single building left undamaged."
The Georgian government said it will try to protect Russian peacekeepers who are in the disputed region. However Russia claims 10 Russian peacekeepers have already been killed.
As the fighting escalates Georgia says it will withdraw 1,000 troops from Iraq and redeploy them to the region.
Nato, the US and the EU are calling for an immediate end to hostilities.
Georgia claims to have shot down five Russian war planes as the two countries fight for control of the breakaway province of South Ossetia.
Russian President Dmitry Medvedev has vowed to protect Russian citizens in the region.
Medvedev said: "In accordance with the constitution and the federal law, I, as president of Russia, am obliged to protect the lives and dignity of Russian citizens wherever they are located," Mr Medvedev said in televised remarks.
"We won't allow the death of our compatriots to go unpunished."
Georgian troops are currently observing a three-hour ceasefire to let civilians leave the besieged capital, Tskhinvali.
Saakashvili said most of South Ossetia had been "liberated" in an overnight offensive.
"Most of South Ossetia's territory is liberated and is controlled by Georgia," Saakashvili said in televised comments today.
"Russian flights are ongoing in the centre of Tskhinvali (the South Ossetian capital)... I demand Russia stop bombardment of peaceful Georgian cities."
Video from Russia Today
Georgia launches offensive in South Ossetia
By Shaun Walker in Moscow
According to the Russian agency Interfax, a large group of Georgian soldiers moved towards the breakaway capital, Tskhinvali, late yesterday evening.
The separatist President, Eduard Kokoity, told the agency that "the storming of Tskhinvali has started" and said that separatist forces were engaged with the Georgian army on the roads into the city. A statement on the separatist government's website said: "The assault is coming from all directions."
The fear is that Russia could be drawn into the conflict, with previous foreign ministry statements saying that Russia could not remain "indifferent" to an armed skirmish on its southern border. Already late last night there were reports that hundreds of volunteers were on their way from North Ossetia, which is part of Russia, through the Caucasus Mountains to join their ethnic kin in South Ossetia. The leadership of Abkhazia, Georgia's other breakaway state, said that 1,000 volunteers from Abkhazia were also on their way.
South Ossetia is a tiny territory with a population of around 50,000, which broke away from Georgia after the collapse of the Soviet Union. Most of the region is under the control of separatist authorities but the central Georgian government in Tbilisi controls several villages. Tensions have been high in recent months, with frequent exchanges of fire between the sides, but so far all-out war has been avoided. An exchange of fire on Wednesday night left at least one person dead and many injured.
The West has supported Georgian President Mikhail Saakashvili, who wants to bring his country out of Russia's orbit and into Nato, in his drive to reintegrate the breakaway regions of South Ossetia and Abkhazia into Georgia's fold. However, any military action could harm the country's chances of Nato accession. Russia has provided financial support to the separatist authorities.
It now seems the Georgians may have tired of negotiations and decided to take matters into their own hands. But the timing is bizarre. Negotiations between the separatist authorities and a Georgian minister were planned for this afternoon, and the attack on Tskhinvali came just hours after Mr Saakashvili had announced a unilateral ceasefire on live television.
"I want to acknowledge that several hours ago I, as a supreme commander, have issued a very painful order not to return fire in response to a very intensive shelling [of Georgian villages]," said the Georgian President yesterday evening.
But the ceasefire lasted only hours and Mr Kokoity called Mr Saakashvili's ceasefire a "despicable and treacherous" ruse.
"Despite our call for peace and a unilateral ceasefire, separatists continued the shelling of Georgian villages," said Georgian commander Mamuka Kurashvili. "We are forced to restore constitutional order in the whole region."
And Moscow reacted furiously to the news. "The actions by Georgia in South Ossetia bear witness to the fact that the leadership of that country can no longer be trusted," said a foreign ministry statement.
The Georgian government said it had information about "hundreds of mercenaries, tanks and other equipment" entering South Ossetia through the Roki tunnel from Russia.
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