Russian troops repelled Georgian forces from the breakaway regions
Russia has taken a series of diplomatic steps in an apparent effort to ease tensions with the West over this month's conflict in Georgia.
President Dmitry Medvedev told UK Prime Minister Gordon Brown Moscow wanted more monitors from Europe's security body in Georgia, the Kremlin said.
Separately, Russian and German foreign ministers agreed to seek to calm tensions over the crisis, Moscow said.
The issue is set to dominate the agenda of an EU meeting on Monday.
French Foreign Minister Bernard Kouchner said earlier this week that the bloc was considering sanctions "and many other means" against Russia over the crisis.
But he said he hoped the matter would "be solved by negotiation".
Moscow's military action in Georgia and its subsequent recognition of independence of Abkhazia and South Ossetia - Georgia's two rebel regions - have angered the West.
Moscow has defended its actions, saying they prevented a "genocide" in South Ossetia.
However, after the inflammatory rhetoric Russia now appears to have decided it is time for a bit of diplomacy, the BBC's Rupert Wingfield-Hayes in Moscow says.
During Saturday's telephone conversation with Mr Brown, President Medvedev said Russia was "in favour of the deployment of additional OSCE [Organisation for Security and Co-operation in Europe] monitors in the security zone" in Georgia, the Kremlin statement said.
It said observers in the security zone would provide "impartial monitoring" of Tbilisi's actions.
Earlier this month, the OSCE decided to increase the number of its military observers by up 100 in Georgia.
Mr Medvedev also said that Russia recognised Georgia's regions of South Ossetia and Abkhazia because of Tbilisi's aggression.
He said that the Georgian move "fundamentally altered the conditions in which, during 17 years, attempts were made to settle the relations between South Ossetia, Abkhazia and Georgia," the statement said.
In a separate development, Russian Foreign Minister Sergei Lavrov spoke to his German counterpart, Frank-Walter Steinmeier.
They both "agreed on the need to put an end to attempts to use the situation surrounding Georgia... to raise tensions in Europe by speculating on non-existent threats concerning other post-Soviet countries," a Russian foreign ministry statement said.
The conflict 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. Russian troops continued their operation, advancing deep inside Georgia's territory.
An EU-brokered ceasefire brought a formal end to the conflict five days later, although each side has accused the other of breaking the agreement.
Russia has since withdrawn the bulk of its force and says the troops left behind are serving as peacekeepers.
Georgia has described them as an occupation force, announcing that it is cutting diplomatic relations with Moscow.