Moscow says it will complete its troop pullout from the buffer zones by 10 October.
EU OBSERVERS IN GEORGIA
More than 200 unarmed observers from 22 EU nations
HQ in Tbilisi, with additional four field offices
Oversee Russia's pullout from "buffer zones" by 10 Oct
Deployed under a French-brokered peace deal
Mission's initial duration is 12 months
On Wednesday, Russian President Dmitry Medvedev said Moscow would abide by its pledge.
"Russian peacekeepers will be withdrawn from Georgia within the agreed dates," he said at a meeting with Spanish Prime Minister Jose Luis Rodriguez Zapatero in St Petersburg.
On Tuesday, EU foreign policy chief Javier Solana said he was "optimistic that all the parties [would] comply" with a French-brokered peace plan between Moscow and Tbilisi.
The plan set 1 October as the date for EU monitors to take up positions inside the buffer zones.
Unarmed observers from the EU Monitoring Mission (EUMM) entered the buffer zone at a Russian military checkpoint near the village of Kvenatkotsa, some 20km (12 miles) west of the Georgian town of Gori.
The observers - travelling in light armoured vehicles - were first stopped by the Russians, but after a brief conversation were allowed to move through.
EU observers pass through Mukhrani, 20km from the town of Gori
Another EU patrol moved into the buffer zone after passing through a Russian checkpoint in Karaleti, north of Gori.
But several other EU teams did not even try to enter the buffer zone, because the Russian troops had said they would not be allowed in for "security reasons", says the BBC's Richard Galpin, in Mukhrani, close to the buffer zone.
The EUMM's head, Hansjoerg Haber, said he would seek to "clarify" the situation, adding that political assurances about his teams' deployment had been given by the Kremlin.
A British member of the team said the EU monitors wanted to take a softly-softly approach on the first day as negotiations continued at a higher level, our correspondent says.
Later on Wednesday, an EUMM spokesman said that the observers' first day had gone "smoothly".
"Patrols made first contact with authorities and population," the spokesman was quoted by Reuters as saying.
The uncertainty was first triggered on Tuesday, when Lt Col Vitaly Manushko, spokesman for Russian forces in South Ossetia, said the monitors would only be able to patrol "up to the southern limit of the security zone".
Some 12 EU patrols were operating on Wednesday.
Observers from 22 EU nations are deployed in Georgia, many of whom are French gendarmes. There are also experts on human rights and legal issues.
The Russian pull-back was agreed in the ceasefire deal brokered by French President Nicolas Sarkozy.
But Russia plans to keep nearly 8,000 troops in Abkhazia and South Ossetia, which it has recognised as independent states.
Western leaders have condemned both the buffer zones and Russia's recognition of the two regions.
The EU wants its observers to have access to the breakaway regions, but Russia has repeatedly refused to guarantee that.
As the EU started to deploy its monitors to Georgia, it was confirmed that an international donors' conference would be held in Brussels next month.
The United States has pledged $1bn in aid to Georgia, and Europe is expected to match that sum when ministers from 27 EU countries gather at the conference.
The European Commission has already agreed a package worth $700m over three years to repair Georgia's infrastructure and revive the economy following the conflict.
The fighting in the region began on 7 August when Georgia tried to retake South Ossetia by force after a series of lower-level clashes.
Russia launched a counter-attack and the Georgian troops were ejected from both South Ossetia and Abkhazia several days later.
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