The West is demanding an immediate Russian pullout from Georgia
Russia has circulated its own draft UN Security Council resolution aimed at bringing peace to Georgia, a day after rejecting a rival French document.
The Russian text endorses a six-point ceasefire plan signed by Moscow and Tbilisi last week.
Moscow earlier said it could not back the French draft that demanded an immediate Russian pullout from Georgia.
The US and its European allies have criticised Russia for keeping its troops in Georgia despite the truce.
All this shows how far apart Russia is from the West, says the BBC's Laura Trevelyan at the UN headquarters in New York.
Russia is one of the five veto-wielding nations of the 15-member Council who can block UN resolutions.
The conflict broke out on 7 August when Georgia launched an assault to wrest back control of the Moscow-backed separatist region of South Ossetia, triggering a counter-offensive by Russian troops who advanced beyond South Ossetia into Georgia's heartland.
US President George W Bush reiterated on Wednesday that South Ossetia and another breakaway region, Abkhazia, remained part of Georgia.
In a separate development, Russia issued new, reduced casualty figures for the Georgian conflict, with 133 civilians now listed as dead in Georgia's breakaway region of South Ossetia.
The figure is far lower than the 1,600 people Russia initially said had died.
'Additional security measures'
The Russian draft resolution restates the terms of the six-point ceasefire deal brokered by French President Nicolas Sarkozy and later signed by Russian President Dmitry Medvedev and Georgian President Mikhail Saakashvili.
The text "calls upon the parties concerned to implement the above mentioned plan in good faith".
Moscow also argues that the truce allows it to implement unspecified "additional security measures" before pulling out of Georgia.
France had originally negotiated with Russia a resolution similar to the one now introduced by Moscow but later shelved it.
European countries and the US say Russia is not honouring the ceasefire plan and should withdraw its forces from Georgia as soon as possible, our correspondent says.
She adds that Western diplomats say they want to expose Russia.
On Tuesday, Russia rejected the French draft saying it contradicted the terms of last week's ceasefire deal.
That text called on Russia to pull back its forces to the positions held before the current conflict.
But Moscow said the truce allowed its troops to stay in a buffer zone on the Georgia side of South Ossetia's border.
At the UN, Russian ambassador Vitaly Churkin also objected to language in the draft reaffirming Georgia's territorial integrity, saying South Ossetia and Abkhazia did not want to be part of Georgia.
The conflict broke out on 7 August when Georgia launched an assault to wrest back control of the Moscow-backed breakaway region of South Ossetia, triggering a counter-offensive by Russian troops who advanced beyond South Ossetia into Georgia's heartland.
Georgia says its action was in response to continuous provocation.